/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES Problem 1: (VAR I P V V1 V2 X X1 X2 X3 Y Z) (RULES U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ) Problem 1: Dependency Pairs Processor: -> Pairs: U11#(active(X1),X2) -> U11#(X1,X2) U11#(mark(X1),X2) -> U11#(X1,X2) U11#(X1,active(X2)) -> U11#(X1,X2) U11#(X1,mark(X2)) -> U11#(X1,X2) U12#(active(X1),X2) -> U12#(X1,X2) U12#(mark(X1),X2) -> U12#(X1,X2) U12#(X1,active(X2)) -> U12#(X1,X2) U12#(X1,mark(X2)) -> U12#(X1,X2) U13#(active(X)) -> U13#(X) U13#(mark(X)) -> U13#(X) U21#(active(X1),X2,X3) -> U21#(X1,X2,X3) U21#(mark(X1),X2,X3) -> U21#(X1,X2,X3) U21#(X1,active(X2),X3) -> U21#(X1,X2,X3) U21#(X1,mark(X2),X3) -> U21#(X1,X2,X3) U21#(X1,X2,active(X3)) -> U21#(X1,X2,X3) U21#(X1,X2,mark(X3)) -> U21#(X1,X2,X3) U22#(active(X1),X2,X3) -> U22#(X1,X2,X3) U22#(mark(X1),X2,X3) -> U22#(X1,X2,X3) U22#(X1,active(X2),X3) -> U22#(X1,X2,X3) U22#(X1,mark(X2),X3) -> U22#(X1,X2,X3) U22#(X1,X2,active(X3)) -> U22#(X1,X2,X3) U22#(X1,X2,mark(X3)) -> U22#(X1,X2,X3) U23#(active(X1),X2,X3) -> U23#(X1,X2,X3) U23#(mark(X1),X2,X3) -> U23#(X1,X2,X3) U23#(X1,active(X2),X3) -> U23#(X1,X2,X3) U23#(X1,mark(X2),X3) -> U23#(X1,X2,X3) U23#(X1,X2,active(X3)) -> U23#(X1,X2,X3) U23#(X1,X2,mark(X3)) -> U23#(X1,X2,X3) U24#(active(X1),X2,X3) -> U24#(X1,X2,X3) U24#(mark(X1),X2,X3) -> U24#(X1,X2,X3) U24#(X1,active(X2),X3) -> U24#(X1,X2,X3) U24#(X1,mark(X2),X3) -> U24#(X1,X2,X3) U24#(X1,X2,active(X3)) -> U24#(X1,X2,X3) U24#(X1,X2,mark(X3)) -> U24#(X1,X2,X3) U25#(active(X1),X2) -> U25#(X1,X2) U25#(mark(X1),X2) -> U25#(X1,X2) U25#(X1,active(X2)) -> U25#(X1,X2) U25#(X1,mark(X2)) -> U25#(X1,X2) U26#(active(X)) -> U26#(X) U26#(mark(X)) -> U26#(X) U31#(active(X1),X2) -> U31#(X1,X2) U31#(mark(X1),X2) -> U31#(X1,X2) U31#(X1,active(X2)) -> U31#(X1,X2) U31#(X1,mark(X2)) -> U31#(X1,X2) U32#(active(X1),X2) -> U32#(X1,X2) U32#(mark(X1),X2) -> U32#(X1,X2) U32#(X1,active(X2)) -> U32#(X1,X2) U32#(X1,mark(X2)) -> U32#(X1,X2) U33#(active(X)) -> U33#(X) U33#(mark(X)) -> U33#(X) U41#(active(X1),X2,X3) -> U41#(X1,X2,X3) U41#(mark(X1),X2,X3) -> U41#(X1,X2,X3) U41#(X1,active(X2),X3) -> U41#(X1,X2,X3) U41#(X1,mark(X2),X3) -> U41#(X1,X2,X3) U41#(X1,X2,active(X3)) -> U41#(X1,X2,X3) U41#(X1,X2,mark(X3)) -> U41#(X1,X2,X3) U42#(active(X1),X2,X3) -> U42#(X1,X2,X3) U42#(mark(X1),X2,X3) -> U42#(X1,X2,X3) U42#(X1,active(X2),X3) -> U42#(X1,X2,X3) U42#(X1,mark(X2),X3) -> U42#(X1,X2,X3) U42#(X1,X2,active(X3)) -> U42#(X1,X2,X3) U42#(X1,X2,mark(X3)) -> U42#(X1,X2,X3) U43#(active(X1),X2,X3) -> U43#(X1,X2,X3) U43#(mark(X1),X2,X3) -> U43#(X1,X2,X3) U43#(X1,active(X2),X3) -> U43#(X1,X2,X3) U43#(X1,mark(X2),X3) -> U43#(X1,X2,X3) U43#(X1,X2,active(X3)) -> U43#(X1,X2,X3) U43#(X1,X2,mark(X3)) -> U43#(X1,X2,X3) U44#(active(X1),X2,X3) -> U44#(X1,X2,X3) U44#(mark(X1),X2,X3) -> U44#(X1,X2,X3) U44#(X1,active(X2),X3) -> U44#(X1,X2,X3) U44#(X1,mark(X2),X3) -> U44#(X1,X2,X3) U44#(X1,X2,active(X3)) -> U44#(X1,X2,X3) U44#(X1,X2,mark(X3)) -> U44#(X1,X2,X3) U45#(active(X1),X2) -> U45#(X1,X2) U45#(mark(X1),X2) -> U45#(X1,X2) U45#(X1,active(X2)) -> U45#(X1,X2) U45#(X1,mark(X2)) -> U45#(X1,X2) U46#(active(X)) -> U46#(X) U46#(mark(X)) -> U46#(X) U51#(active(X1),X2,X3) -> U51#(X1,X2,X3) U51#(mark(X1),X2,X3) -> U51#(X1,X2,X3) U51#(X1,active(X2),X3) -> U51#(X1,X2,X3) U51#(X1,mark(X2),X3) -> U51#(X1,X2,X3) U51#(X1,X2,active(X3)) -> U51#(X1,X2,X3) U51#(X1,X2,mark(X3)) -> U51#(X1,X2,X3) U52#(active(X1),X2,X3) -> U52#(X1,X2,X3) U52#(mark(X1),X2,X3) -> U52#(X1,X2,X3) U52#(X1,active(X2),X3) -> U52#(X1,X2,X3) U52#(X1,mark(X2),X3) -> U52#(X1,X2,X3) U52#(X1,X2,active(X3)) -> U52#(X1,X2,X3) U52#(X1,X2,mark(X3)) -> U52#(X1,X2,X3) U53#(active(X1),X2,X3) -> U53#(X1,X2,X3) U53#(mark(X1),X2,X3) -> U53#(X1,X2,X3) U53#(X1,active(X2),X3) -> U53#(X1,X2,X3) U53#(X1,mark(X2),X3) -> U53#(X1,X2,X3) U53#(X1,X2,active(X3)) -> U53#(X1,X2,X3) U53#(X1,X2,mark(X3)) -> U53#(X1,X2,X3) U54#(active(X1),X2,X3) -> U54#(X1,X2,X3) U54#(mark(X1),X2,X3) -> U54#(X1,X2,X3) U54#(X1,active(X2),X3) -> U54#(X1,X2,X3) U54#(X1,mark(X2),X3) -> U54#(X1,X2,X3) U54#(X1,X2,active(X3)) -> U54#(X1,X2,X3) U54#(X1,X2,mark(X3)) -> U54#(X1,X2,X3) U55#(active(X1),X2) -> U55#(X1,X2) U55#(mark(X1),X2) -> U55#(X1,X2) U55#(X1,active(X2)) -> U55#(X1,X2) U55#(X1,mark(X2)) -> U55#(X1,X2) U56#(active(X)) -> U56#(X) U56#(mark(X)) -> U56#(X) U61#(active(X1),X2) -> U61#(X1,X2) U61#(mark(X1),X2) -> U61#(X1,X2) U61#(X1,active(X2)) -> U61#(X1,X2) U61#(X1,mark(X2)) -> U61#(X1,X2) U62#(active(X1),X2) -> U62#(X1,X2) U62#(mark(X1),X2) -> U62#(X1,X2) U62#(X1,active(X2)) -> U62#(X1,X2) U62#(X1,mark(X2)) -> U62#(X1,X2) U63#(active(X)) -> U63#(X) U63#(mark(X)) -> U63#(X) U71#(active(X1),X2,X3) -> U71#(X1,X2,X3) U71#(mark(X1),X2,X3) -> U71#(X1,X2,X3) U71#(X1,active(X2),X3) -> U71#(X1,X2,X3) U71#(X1,mark(X2),X3) -> U71#(X1,X2,X3) U71#(X1,X2,active(X3)) -> U71#(X1,X2,X3) U71#(X1,X2,mark(X3)) -> U71#(X1,X2,X3) U72#(active(X1),X2) -> U72#(X1,X2) U72#(mark(X1),X2) -> U72#(X1,X2) U72#(X1,active(X2)) -> U72#(X1,X2) U72#(X1,mark(X2)) -> U72#(X1,X2) U73#(active(X1),X2) -> U73#(X1,X2) U73#(mark(X1),X2) -> U73#(X1,X2) U73#(X1,active(X2)) -> U73#(X1,X2) U73#(X1,mark(X2)) -> U73#(X1,X2) U74#(active(X)) -> U74#(X) U74#(mark(X)) -> U74#(X) U81#(active(X1),X2) -> U81#(X1,X2) U81#(mark(X1),X2) -> U81#(X1,X2) U81#(X1,active(X2)) -> U81#(X1,X2) U81#(X1,mark(X2)) -> U81#(X1,X2) U82#(active(X1),X2) -> U82#(X1,X2) U82#(mark(X1),X2) -> U82#(X1,X2) U82#(X1,active(X2)) -> U82#(X1,X2) U82#(X1,mark(X2)) -> U82#(X1,X2) U83#(active(X)) -> U83#(X) U83#(mark(X)) -> U83#(X) U91#(active(X1),X2) -> U91#(X1,X2) U91#(mark(X1),X2) -> U91#(X1,X2) U91#(X1,active(X2)) -> U91#(X1,X2) U91#(X1,mark(X2)) -> U91#(X1,X2) U92#(active(X)) -> U92#(X) U92#(mark(X)) -> U92#(X) __#(active(X1),X2) -> __#(X1,X2) __#(mark(X1),X2) -> __#(X1,X2) __#(X1,active(X2)) -> __#(X1,X2) __#(X1,mark(X2)) -> __#(X1,X2) ACTIVE(U11(tt,V)) -> U12#(isPalListKind(V),V) ACTIVE(U11(tt,V)) -> ISPALLISTKIND(V) ACTIVE(U11(tt,V)) -> MARK(U12(isPalListKind(V),V)) ACTIVE(U12(tt,V)) -> U13#(isNeList(V)) ACTIVE(U12(tt,V)) -> ISNELIST(V) ACTIVE(U12(tt,V)) -> MARK(U13(isNeList(V))) ACTIVE(U13(tt)) -> MARK(tt) ACTIVE(U21(tt,V1,V2)) -> U22#(isPalListKind(V1),V1,V2) ACTIVE(U21(tt,V1,V2)) -> ISPALLISTKIND(V1) ACTIVE(U21(tt,V1,V2)) -> MARK(U22(isPalListKind(V1),V1,V2)) ACTIVE(U22(tt,V1,V2)) -> U23#(isPalListKind(V2),V1,V2) ACTIVE(U22(tt,V1,V2)) -> ISPALLISTKIND(V2) ACTIVE(U22(tt,V1,V2)) -> MARK(U23(isPalListKind(V2),V1,V2)) ACTIVE(U23(tt,V1,V2)) -> U24#(isPalListKind(V2),V1,V2) ACTIVE(U23(tt,V1,V2)) -> ISPALLISTKIND(V2) ACTIVE(U23(tt,V1,V2)) -> MARK(U24(isPalListKind(V2),V1,V2)) ACTIVE(U24(tt,V1,V2)) -> U25#(isList(V1),V2) ACTIVE(U24(tt,V1,V2)) -> ISLIST(V1) ACTIVE(U24(tt,V1,V2)) -> MARK(U25(isList(V1),V2)) ACTIVE(U25(tt,V2)) -> U26#(isList(V2)) ACTIVE(U25(tt,V2)) -> ISLIST(V2) ACTIVE(U25(tt,V2)) -> MARK(U26(isList(V2))) ACTIVE(U26(tt)) -> MARK(tt) ACTIVE(U31(tt,V)) -> U32#(isPalListKind(V),V) ACTIVE(U31(tt,V)) -> ISPALLISTKIND(V) ACTIVE(U31(tt,V)) -> MARK(U32(isPalListKind(V),V)) ACTIVE(U32(tt,V)) -> U33#(isQid(V)) ACTIVE(U32(tt,V)) -> ISQID(V) ACTIVE(U32(tt,V)) -> MARK(U33(isQid(V))) ACTIVE(U33(tt)) -> MARK(tt) ACTIVE(U41(tt,V1,V2)) -> U42#(isPalListKind(V1),V1,V2) ACTIVE(U41(tt,V1,V2)) -> ISPALLISTKIND(V1) ACTIVE(U41(tt,V1,V2)) -> MARK(U42(isPalListKind(V1),V1,V2)) ACTIVE(U42(tt,V1,V2)) -> U43#(isPalListKind(V2),V1,V2) ACTIVE(U42(tt,V1,V2)) -> ISPALLISTKIND(V2) ACTIVE(U42(tt,V1,V2)) -> MARK(U43(isPalListKind(V2),V1,V2)) ACTIVE(U43(tt,V1,V2)) -> U44#(isPalListKind(V2),V1,V2) ACTIVE(U43(tt,V1,V2)) -> ISPALLISTKIND(V2) ACTIVE(U43(tt,V1,V2)) -> MARK(U44(isPalListKind(V2),V1,V2)) ACTIVE(U44(tt,V1,V2)) -> U45#(isList(V1),V2) ACTIVE(U44(tt,V1,V2)) -> ISLIST(V1) ACTIVE(U44(tt,V1,V2)) -> MARK(U45(isList(V1),V2)) ACTIVE(U45(tt,V2)) -> U46#(isNeList(V2)) ACTIVE(U45(tt,V2)) -> ISNELIST(V2) ACTIVE(U45(tt,V2)) -> MARK(U46(isNeList(V2))) ACTIVE(U46(tt)) -> MARK(tt) ACTIVE(U51(tt,V1,V2)) -> U52#(isPalListKind(V1),V1,V2) ACTIVE(U51(tt,V1,V2)) -> ISPALLISTKIND(V1) ACTIVE(U51(tt,V1,V2)) -> MARK(U52(isPalListKind(V1),V1,V2)) ACTIVE(U52(tt,V1,V2)) -> U53#(isPalListKind(V2),V1,V2) ACTIVE(U52(tt,V1,V2)) -> ISPALLISTKIND(V2) ACTIVE(U52(tt,V1,V2)) -> MARK(U53(isPalListKind(V2),V1,V2)) ACTIVE(U53(tt,V1,V2)) -> U54#(isPalListKind(V2),V1,V2) ACTIVE(U53(tt,V1,V2)) -> ISPALLISTKIND(V2) ACTIVE(U53(tt,V1,V2)) -> MARK(U54(isPalListKind(V2),V1,V2)) ACTIVE(U54(tt,V1,V2)) -> U55#(isNeList(V1),V2) ACTIVE(U54(tt,V1,V2)) -> ISNELIST(V1) ACTIVE(U54(tt,V1,V2)) -> MARK(U55(isNeList(V1),V2)) ACTIVE(U55(tt,V2)) -> U56#(isList(V2)) ACTIVE(U55(tt,V2)) -> ISLIST(V2) ACTIVE(U55(tt,V2)) -> MARK(U56(isList(V2))) ACTIVE(U56(tt)) -> MARK(tt) ACTIVE(U61(tt,V)) -> U62#(isPalListKind(V),V) ACTIVE(U61(tt,V)) -> ISPALLISTKIND(V) ACTIVE(U61(tt,V)) -> MARK(U62(isPalListKind(V),V)) ACTIVE(U62(tt,V)) -> U63#(isQid(V)) ACTIVE(U62(tt,V)) -> ISQID(V) ACTIVE(U62(tt,V)) -> MARK(U63(isQid(V))) ACTIVE(U63(tt)) -> MARK(tt) ACTIVE(U71(tt,I,P)) -> U72#(isPalListKind(I),P) ACTIVE(U71(tt,I,P)) -> ISPALLISTKIND(I) ACTIVE(U71(tt,I,P)) -> MARK(U72(isPalListKind(I),P)) ACTIVE(U72(tt,P)) -> U73#(isPal(P),P) ACTIVE(U72(tt,P)) -> ISPAL(P) ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> U74#(isPalListKind(P)) ACTIVE(U73(tt,P)) -> ISPALLISTKIND(P) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U74(tt)) -> MARK(tt) ACTIVE(U81(tt,V)) -> U82#(isPalListKind(V),V) ACTIVE(U81(tt,V)) -> ISPALLISTKIND(V) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> U83#(isNePal(V)) ACTIVE(U82(tt,V)) -> ISNEPAL(V) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U83(tt)) -> MARK(tt) ACTIVE(U91(tt,V2)) -> U92#(isPalListKind(V2)) ACTIVE(U91(tt,V2)) -> ISPALLISTKIND(V2) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(U92(tt)) -> MARK(tt) ACTIVE(__(__(X,Y),Z)) -> __#(X,__(Y,Z)) ACTIVE(__(__(X,Y),Z)) -> __#(Y,Z) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> U21#(isPalListKind(V1),V1,V2) ACTIVE(isList(__(V1,V2))) -> ISPALLISTKIND(V1) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(nil)) -> MARK(tt) ACTIVE(isList(V)) -> U11#(isPalListKind(V),V) ACTIVE(isList(V)) -> ISPALLISTKIND(V) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> U41#(isPalListKind(V1),V1,V2) ACTIVE(isNeList(__(V1,V2))) -> U51#(isPalListKind(V1),V1,V2) ACTIVE(isNeList(__(V1,V2))) -> ISPALLISTKIND(V1) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> U31#(isPalListKind(V),V) ACTIVE(isNeList(V)) -> ISPALLISTKIND(V) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> U71#(isQid(I),I,P) ACTIVE(isNePal(__(I,__(P,I)))) -> ISQID(I) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> U61#(isPalListKind(V),V) ACTIVE(isNePal(V)) -> ISPALLISTKIND(V) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(nil)) -> MARK(tt) ACTIVE(isPal(V)) -> U81#(isPalListKind(V),V) ACTIVE(isPal(V)) -> ISPALLISTKIND(V) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> U91#(isPalListKind(V1),V2) ACTIVE(isPalListKind(__(V1,V2))) -> ISPALLISTKIND(V1) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) ACTIVE(isPalListKind(a)) -> MARK(tt) ACTIVE(isPalListKind(e)) -> MARK(tt) ACTIVE(isPalListKind(i)) -> MARK(tt) ACTIVE(isPalListKind(nil)) -> MARK(tt) ACTIVE(isPalListKind(o)) -> MARK(tt) ACTIVE(isPalListKind(u)) -> MARK(tt) ACTIVE(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(active(X)) -> ISLIST(X) ISLIST(mark(X)) -> ISLIST(X) ISNELIST(active(X)) -> ISNELIST(X) ISNELIST(mark(X)) -> ISNELIST(X) ISNEPAL(active(X)) -> ISNEPAL(X) ISNEPAL(mark(X)) -> ISNEPAL(X) ISPAL(active(X)) -> ISPAL(X) ISPAL(mark(X)) -> ISPAL(X) ISPALLISTKIND(active(X)) -> ISPALLISTKIND(X) ISPALLISTKIND(mark(X)) -> ISPALLISTKIND(X) ISQID(active(X)) -> ISQID(X) ISQID(mark(X)) -> ISQID(X) MARK(U11(X1,X2)) -> U11#(mark(X1),X2) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> U12#(mark(X1),X2) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> U13#(mark(X)) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> U21#(mark(X1),X2,X3) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> U22#(mark(X1),X2,X3) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> U23#(mark(X1),X2,X3) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> U24#(mark(X1),X2,X3) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> U25#(mark(X1),X2) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> U26#(mark(X)) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> U31#(mark(X1),X2) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> U32#(mark(X1),X2) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> U33#(mark(X)) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> U41#(mark(X1),X2,X3) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> U42#(mark(X1),X2,X3) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> U43#(mark(X1),X2,X3) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> U44#(mark(X1),X2,X3) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> U45#(mark(X1),X2) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> U46#(mark(X)) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> U51#(mark(X1),X2,X3) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> U52#(mark(X1),X2,X3) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> U53#(mark(X1),X2,X3) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> U54#(mark(X1),X2,X3) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> U55#(mark(X1),X2) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> U56#(mark(X)) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> U61#(mark(X1),X2) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> U62#(mark(X1),X2) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> U63#(mark(X)) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> U71#(mark(X1),X2,X3) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> U72#(mark(X1),X2) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> U73#(mark(X1),X2) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> U74#(mark(X)) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> U81#(mark(X1),X2) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> U82#(mark(X1),X2) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> U83#(mark(X)) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> U91#(mark(X1),X2) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> U92#(mark(X)) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> __#(mark(X1),mark(X2)) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1: SCC Processor: -> Pairs: U11#(active(X1),X2) -> U11#(X1,X2) U11#(mark(X1),X2) -> U11#(X1,X2) U11#(X1,active(X2)) -> U11#(X1,X2) U11#(X1,mark(X2)) -> U11#(X1,X2) U12#(active(X1),X2) -> U12#(X1,X2) U12#(mark(X1),X2) -> U12#(X1,X2) U12#(X1,active(X2)) -> U12#(X1,X2) U12#(X1,mark(X2)) -> U12#(X1,X2) U13#(active(X)) -> U13#(X) U13#(mark(X)) -> U13#(X) U21#(active(X1),X2,X3) -> U21#(X1,X2,X3) U21#(mark(X1),X2,X3) -> U21#(X1,X2,X3) U21#(X1,active(X2),X3) -> U21#(X1,X2,X3) U21#(X1,mark(X2),X3) -> U21#(X1,X2,X3) U21#(X1,X2,active(X3)) -> U21#(X1,X2,X3) U21#(X1,X2,mark(X3)) -> U21#(X1,X2,X3) U22#(active(X1),X2,X3) -> U22#(X1,X2,X3) U22#(mark(X1),X2,X3) -> U22#(X1,X2,X3) U22#(X1,active(X2),X3) -> U22#(X1,X2,X3) U22#(X1,mark(X2),X3) -> U22#(X1,X2,X3) U22#(X1,X2,active(X3)) -> U22#(X1,X2,X3) U22#(X1,X2,mark(X3)) -> U22#(X1,X2,X3) U23#(active(X1),X2,X3) -> U23#(X1,X2,X3) U23#(mark(X1),X2,X3) -> U23#(X1,X2,X3) U23#(X1,active(X2),X3) -> U23#(X1,X2,X3) U23#(X1,mark(X2),X3) -> U23#(X1,X2,X3) U23#(X1,X2,active(X3)) -> U23#(X1,X2,X3) U23#(X1,X2,mark(X3)) -> U23#(X1,X2,X3) U24#(active(X1),X2,X3) -> U24#(X1,X2,X3) U24#(mark(X1),X2,X3) -> U24#(X1,X2,X3) U24#(X1,active(X2),X3) -> U24#(X1,X2,X3) U24#(X1,mark(X2),X3) -> U24#(X1,X2,X3) U24#(X1,X2,active(X3)) -> U24#(X1,X2,X3) U24#(X1,X2,mark(X3)) -> U24#(X1,X2,X3) U25#(active(X1),X2) -> U25#(X1,X2) U25#(mark(X1),X2) -> U25#(X1,X2) U25#(X1,active(X2)) -> U25#(X1,X2) U25#(X1,mark(X2)) -> U25#(X1,X2) U26#(active(X)) -> U26#(X) U26#(mark(X)) -> U26#(X) U31#(active(X1),X2) -> U31#(X1,X2) U31#(mark(X1),X2) -> U31#(X1,X2) U31#(X1,active(X2)) -> U31#(X1,X2) U31#(X1,mark(X2)) -> U31#(X1,X2) U32#(active(X1),X2) -> U32#(X1,X2) U32#(mark(X1),X2) -> U32#(X1,X2) U32#(X1,active(X2)) -> U32#(X1,X2) U32#(X1,mark(X2)) -> U32#(X1,X2) U33#(active(X)) -> U33#(X) U33#(mark(X)) -> U33#(X) U41#(active(X1),X2,X3) -> U41#(X1,X2,X3) U41#(mark(X1),X2,X3) -> U41#(X1,X2,X3) U41#(X1,active(X2),X3) -> U41#(X1,X2,X3) U41#(X1,mark(X2),X3) -> U41#(X1,X2,X3) U41#(X1,X2,active(X3)) -> U41#(X1,X2,X3) U41#(X1,X2,mark(X3)) -> U41#(X1,X2,X3) U42#(active(X1),X2,X3) -> U42#(X1,X2,X3) U42#(mark(X1),X2,X3) -> U42#(X1,X2,X3) U42#(X1,active(X2),X3) -> U42#(X1,X2,X3) U42#(X1,mark(X2),X3) -> U42#(X1,X2,X3) U42#(X1,X2,active(X3)) -> U42#(X1,X2,X3) U42#(X1,X2,mark(X3)) -> U42#(X1,X2,X3) U43#(active(X1),X2,X3) -> U43#(X1,X2,X3) U43#(mark(X1),X2,X3) -> U43#(X1,X2,X3) U43#(X1,active(X2),X3) -> U43#(X1,X2,X3) U43#(X1,mark(X2),X3) -> U43#(X1,X2,X3) U43#(X1,X2,active(X3)) -> U43#(X1,X2,X3) U43#(X1,X2,mark(X3)) -> U43#(X1,X2,X3) U44#(active(X1),X2,X3) -> U44#(X1,X2,X3) U44#(mark(X1),X2,X3) -> U44#(X1,X2,X3) U44#(X1,active(X2),X3) -> U44#(X1,X2,X3) U44#(X1,mark(X2),X3) -> U44#(X1,X2,X3) U44#(X1,X2,active(X3)) -> U44#(X1,X2,X3) U44#(X1,X2,mark(X3)) -> U44#(X1,X2,X3) U45#(active(X1),X2) -> U45#(X1,X2) U45#(mark(X1),X2) -> U45#(X1,X2) U45#(X1,active(X2)) -> U45#(X1,X2) U45#(X1,mark(X2)) -> U45#(X1,X2) U46#(active(X)) -> U46#(X) U46#(mark(X)) -> U46#(X) U51#(active(X1),X2,X3) -> U51#(X1,X2,X3) U51#(mark(X1),X2,X3) -> U51#(X1,X2,X3) U51#(X1,active(X2),X3) -> U51#(X1,X2,X3) U51#(X1,mark(X2),X3) -> U51#(X1,X2,X3) U51#(X1,X2,active(X3)) -> U51#(X1,X2,X3) U51#(X1,X2,mark(X3)) -> U51#(X1,X2,X3) U52#(active(X1),X2,X3) -> U52#(X1,X2,X3) U52#(mark(X1),X2,X3) -> U52#(X1,X2,X3) U52#(X1,active(X2),X3) -> U52#(X1,X2,X3) U52#(X1,mark(X2),X3) -> U52#(X1,X2,X3) U52#(X1,X2,active(X3)) -> U52#(X1,X2,X3) U52#(X1,X2,mark(X3)) -> U52#(X1,X2,X3) U53#(active(X1),X2,X3) -> U53#(X1,X2,X3) U53#(mark(X1),X2,X3) -> U53#(X1,X2,X3) U53#(X1,active(X2),X3) -> U53#(X1,X2,X3) U53#(X1,mark(X2),X3) -> U53#(X1,X2,X3) U53#(X1,X2,active(X3)) -> U53#(X1,X2,X3) U53#(X1,X2,mark(X3)) -> U53#(X1,X2,X3) U54#(active(X1),X2,X3) -> U54#(X1,X2,X3) U54#(mark(X1),X2,X3) -> U54#(X1,X2,X3) U54#(X1,active(X2),X3) -> U54#(X1,X2,X3) U54#(X1,mark(X2),X3) -> U54#(X1,X2,X3) U54#(X1,X2,active(X3)) -> U54#(X1,X2,X3) U54#(X1,X2,mark(X3)) -> U54#(X1,X2,X3) U55#(active(X1),X2) -> U55#(X1,X2) U55#(mark(X1),X2) -> U55#(X1,X2) U55#(X1,active(X2)) -> U55#(X1,X2) U55#(X1,mark(X2)) -> U55#(X1,X2) U56#(active(X)) -> U56#(X) U56#(mark(X)) -> U56#(X) U61#(active(X1),X2) -> U61#(X1,X2) U61#(mark(X1),X2) -> U61#(X1,X2) U61#(X1,active(X2)) -> U61#(X1,X2) U61#(X1,mark(X2)) -> U61#(X1,X2) U62#(active(X1),X2) -> U62#(X1,X2) U62#(mark(X1),X2) -> U62#(X1,X2) U62#(X1,active(X2)) -> U62#(X1,X2) U62#(X1,mark(X2)) -> U62#(X1,X2) U63#(active(X)) -> U63#(X) U63#(mark(X)) -> U63#(X) U71#(active(X1),X2,X3) -> U71#(X1,X2,X3) U71#(mark(X1),X2,X3) -> U71#(X1,X2,X3) U71#(X1,active(X2),X3) -> U71#(X1,X2,X3) U71#(X1,mark(X2),X3) -> U71#(X1,X2,X3) U71#(X1,X2,active(X3)) -> U71#(X1,X2,X3) U71#(X1,X2,mark(X3)) -> U71#(X1,X2,X3) U72#(active(X1),X2) -> U72#(X1,X2) U72#(mark(X1),X2) -> U72#(X1,X2) U72#(X1,active(X2)) -> U72#(X1,X2) U72#(X1,mark(X2)) -> U72#(X1,X2) U73#(active(X1),X2) -> U73#(X1,X2) U73#(mark(X1),X2) -> U73#(X1,X2) U73#(X1,active(X2)) -> U73#(X1,X2) U73#(X1,mark(X2)) -> U73#(X1,X2) U74#(active(X)) -> U74#(X) U74#(mark(X)) -> U74#(X) U81#(active(X1),X2) -> U81#(X1,X2) U81#(mark(X1),X2) -> U81#(X1,X2) U81#(X1,active(X2)) -> U81#(X1,X2) U81#(X1,mark(X2)) -> U81#(X1,X2) U82#(active(X1),X2) -> U82#(X1,X2) U82#(mark(X1),X2) -> U82#(X1,X2) U82#(X1,active(X2)) -> U82#(X1,X2) U82#(X1,mark(X2)) -> U82#(X1,X2) U83#(active(X)) -> U83#(X) U83#(mark(X)) -> U83#(X) U91#(active(X1),X2) -> U91#(X1,X2) U91#(mark(X1),X2) -> U91#(X1,X2) U91#(X1,active(X2)) -> U91#(X1,X2) U91#(X1,mark(X2)) -> U91#(X1,X2) U92#(active(X)) -> U92#(X) U92#(mark(X)) -> U92#(X) __#(active(X1),X2) -> __#(X1,X2) __#(mark(X1),X2) -> __#(X1,X2) __#(X1,active(X2)) -> __#(X1,X2) __#(X1,mark(X2)) -> __#(X1,X2) ACTIVE(U11(tt,V)) -> U12#(isPalListKind(V),V) ACTIVE(U11(tt,V)) -> ISPALLISTKIND(V) ACTIVE(U11(tt,V)) -> MARK(U12(isPalListKind(V),V)) ACTIVE(U12(tt,V)) -> U13#(isNeList(V)) ACTIVE(U12(tt,V)) -> ISNELIST(V) ACTIVE(U12(tt,V)) -> MARK(U13(isNeList(V))) ACTIVE(U13(tt)) -> MARK(tt) ACTIVE(U21(tt,V1,V2)) -> U22#(isPalListKind(V1),V1,V2) ACTIVE(U21(tt,V1,V2)) -> ISPALLISTKIND(V1) ACTIVE(U21(tt,V1,V2)) -> MARK(U22(isPalListKind(V1),V1,V2)) ACTIVE(U22(tt,V1,V2)) -> U23#(isPalListKind(V2),V1,V2) ACTIVE(U22(tt,V1,V2)) -> ISPALLISTKIND(V2) ACTIVE(U22(tt,V1,V2)) -> MARK(U23(isPalListKind(V2),V1,V2)) ACTIVE(U23(tt,V1,V2)) -> U24#(isPalListKind(V2),V1,V2) ACTIVE(U23(tt,V1,V2)) -> ISPALLISTKIND(V2) ACTIVE(U23(tt,V1,V2)) -> MARK(U24(isPalListKind(V2),V1,V2)) ACTIVE(U24(tt,V1,V2)) -> U25#(isList(V1),V2) ACTIVE(U24(tt,V1,V2)) -> ISLIST(V1) ACTIVE(U24(tt,V1,V2)) -> MARK(U25(isList(V1),V2)) ACTIVE(U25(tt,V2)) -> U26#(isList(V2)) ACTIVE(U25(tt,V2)) -> ISLIST(V2) ACTIVE(U25(tt,V2)) -> MARK(U26(isList(V2))) ACTIVE(U26(tt)) -> MARK(tt) ACTIVE(U31(tt,V)) -> U32#(isPalListKind(V),V) ACTIVE(U31(tt,V)) -> ISPALLISTKIND(V) ACTIVE(U31(tt,V)) -> MARK(U32(isPalListKind(V),V)) ACTIVE(U32(tt,V)) -> U33#(isQid(V)) ACTIVE(U32(tt,V)) -> ISQID(V) ACTIVE(U32(tt,V)) -> MARK(U33(isQid(V))) ACTIVE(U33(tt)) -> MARK(tt) ACTIVE(U41(tt,V1,V2)) -> U42#(isPalListKind(V1),V1,V2) ACTIVE(U41(tt,V1,V2)) -> ISPALLISTKIND(V1) ACTIVE(U41(tt,V1,V2)) -> MARK(U42(isPalListKind(V1),V1,V2)) ACTIVE(U42(tt,V1,V2)) -> U43#(isPalListKind(V2),V1,V2) ACTIVE(U42(tt,V1,V2)) -> ISPALLISTKIND(V2) ACTIVE(U42(tt,V1,V2)) -> MARK(U43(isPalListKind(V2),V1,V2)) ACTIVE(U43(tt,V1,V2)) -> U44#(isPalListKind(V2),V1,V2) ACTIVE(U43(tt,V1,V2)) -> ISPALLISTKIND(V2) ACTIVE(U43(tt,V1,V2)) -> MARK(U44(isPalListKind(V2),V1,V2)) ACTIVE(U44(tt,V1,V2)) -> U45#(isList(V1),V2) ACTIVE(U44(tt,V1,V2)) -> ISLIST(V1) ACTIVE(U44(tt,V1,V2)) -> MARK(U45(isList(V1),V2)) ACTIVE(U45(tt,V2)) -> U46#(isNeList(V2)) ACTIVE(U45(tt,V2)) -> ISNELIST(V2) ACTIVE(U45(tt,V2)) -> MARK(U46(isNeList(V2))) ACTIVE(U46(tt)) -> MARK(tt) ACTIVE(U51(tt,V1,V2)) -> U52#(isPalListKind(V1),V1,V2) ACTIVE(U51(tt,V1,V2)) -> ISPALLISTKIND(V1) ACTIVE(U51(tt,V1,V2)) -> MARK(U52(isPalListKind(V1),V1,V2)) ACTIVE(U52(tt,V1,V2)) -> U53#(isPalListKind(V2),V1,V2) ACTIVE(U52(tt,V1,V2)) -> ISPALLISTKIND(V2) ACTIVE(U52(tt,V1,V2)) -> MARK(U53(isPalListKind(V2),V1,V2)) ACTIVE(U53(tt,V1,V2)) -> U54#(isPalListKind(V2),V1,V2) ACTIVE(U53(tt,V1,V2)) -> ISPALLISTKIND(V2) ACTIVE(U53(tt,V1,V2)) -> MARK(U54(isPalListKind(V2),V1,V2)) ACTIVE(U54(tt,V1,V2)) -> U55#(isNeList(V1),V2) ACTIVE(U54(tt,V1,V2)) -> ISNELIST(V1) ACTIVE(U54(tt,V1,V2)) -> MARK(U55(isNeList(V1),V2)) ACTIVE(U55(tt,V2)) -> U56#(isList(V2)) ACTIVE(U55(tt,V2)) -> ISLIST(V2) ACTIVE(U55(tt,V2)) -> MARK(U56(isList(V2))) ACTIVE(U56(tt)) -> MARK(tt) ACTIVE(U61(tt,V)) -> U62#(isPalListKind(V),V) ACTIVE(U61(tt,V)) -> ISPALLISTKIND(V) ACTIVE(U61(tt,V)) -> MARK(U62(isPalListKind(V),V)) ACTIVE(U62(tt,V)) -> U63#(isQid(V)) ACTIVE(U62(tt,V)) -> ISQID(V) ACTIVE(U62(tt,V)) -> MARK(U63(isQid(V))) ACTIVE(U63(tt)) -> MARK(tt) ACTIVE(U71(tt,I,P)) -> U72#(isPalListKind(I),P) ACTIVE(U71(tt,I,P)) -> ISPALLISTKIND(I) ACTIVE(U71(tt,I,P)) -> MARK(U72(isPalListKind(I),P)) ACTIVE(U72(tt,P)) -> U73#(isPal(P),P) ACTIVE(U72(tt,P)) -> ISPAL(P) ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> U74#(isPalListKind(P)) ACTIVE(U73(tt,P)) -> ISPALLISTKIND(P) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U74(tt)) -> MARK(tt) ACTIVE(U81(tt,V)) -> U82#(isPalListKind(V),V) ACTIVE(U81(tt,V)) -> ISPALLISTKIND(V) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> U83#(isNePal(V)) ACTIVE(U82(tt,V)) -> ISNEPAL(V) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U83(tt)) -> MARK(tt) ACTIVE(U91(tt,V2)) -> U92#(isPalListKind(V2)) ACTIVE(U91(tt,V2)) -> ISPALLISTKIND(V2) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(U92(tt)) -> MARK(tt) ACTIVE(__(__(X,Y),Z)) -> __#(X,__(Y,Z)) ACTIVE(__(__(X,Y),Z)) -> __#(Y,Z) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> U21#(isPalListKind(V1),V1,V2) ACTIVE(isList(__(V1,V2))) -> ISPALLISTKIND(V1) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(nil)) -> MARK(tt) ACTIVE(isList(V)) -> U11#(isPalListKind(V),V) ACTIVE(isList(V)) -> ISPALLISTKIND(V) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> U41#(isPalListKind(V1),V1,V2) ACTIVE(isNeList(__(V1,V2))) -> U51#(isPalListKind(V1),V1,V2) ACTIVE(isNeList(__(V1,V2))) -> ISPALLISTKIND(V1) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> U31#(isPalListKind(V),V) ACTIVE(isNeList(V)) -> ISPALLISTKIND(V) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> U71#(isQid(I),I,P) ACTIVE(isNePal(__(I,__(P,I)))) -> ISQID(I) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> U61#(isPalListKind(V),V) ACTIVE(isNePal(V)) -> ISPALLISTKIND(V) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(nil)) -> MARK(tt) ACTIVE(isPal(V)) -> U81#(isPalListKind(V),V) ACTIVE(isPal(V)) -> ISPALLISTKIND(V) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> U91#(isPalListKind(V1),V2) ACTIVE(isPalListKind(__(V1,V2))) -> ISPALLISTKIND(V1) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) ACTIVE(isPalListKind(a)) -> MARK(tt) ACTIVE(isPalListKind(e)) -> MARK(tt) ACTIVE(isPalListKind(i)) -> MARK(tt) ACTIVE(isPalListKind(nil)) -> MARK(tt) ACTIVE(isPalListKind(o)) -> MARK(tt) ACTIVE(isPalListKind(u)) -> MARK(tt) ACTIVE(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(active(X)) -> ISLIST(X) ISLIST(mark(X)) -> ISLIST(X) ISNELIST(active(X)) -> ISNELIST(X) ISNELIST(mark(X)) -> ISNELIST(X) ISNEPAL(active(X)) -> ISNEPAL(X) ISNEPAL(mark(X)) -> ISNEPAL(X) ISPAL(active(X)) -> ISPAL(X) ISPAL(mark(X)) -> ISPAL(X) ISPALLISTKIND(active(X)) -> ISPALLISTKIND(X) ISPALLISTKIND(mark(X)) -> ISPALLISTKIND(X) ISQID(active(X)) -> ISQID(X) ISQID(mark(X)) -> ISQID(X) MARK(U11(X1,X2)) -> U11#(mark(X1),X2) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> U12#(mark(X1),X2) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> U13#(mark(X)) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> U21#(mark(X1),X2,X3) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> U22#(mark(X1),X2,X3) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> U23#(mark(X1),X2,X3) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> U24#(mark(X1),X2,X3) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> U25#(mark(X1),X2) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> U26#(mark(X)) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> U31#(mark(X1),X2) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> U32#(mark(X1),X2) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> U33#(mark(X)) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> U41#(mark(X1),X2,X3) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> U42#(mark(X1),X2,X3) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> U43#(mark(X1),X2,X3) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> U44#(mark(X1),X2,X3) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> U45#(mark(X1),X2) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> U46#(mark(X)) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> U51#(mark(X1),X2,X3) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> U52#(mark(X1),X2,X3) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> U53#(mark(X1),X2,X3) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> U54#(mark(X1),X2,X3) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> U55#(mark(X1),X2) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> U56#(mark(X)) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> U61#(mark(X1),X2) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> U62#(mark(X1),X2) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> U63#(mark(X)) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> U71#(mark(X1),X2,X3) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> U72#(mark(X1),X2) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> U73#(mark(X1),X2) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> U74#(mark(X)) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> U81#(mark(X1),X2) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> U82#(mark(X1),X2) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> U83#(mark(X)) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> U91#(mark(X1),X2) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> U92#(mark(X)) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> __#(mark(X1),mark(X2)) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ISQID(active(X)) -> ISQID(X) ISQID(mark(X)) -> ISQID(X) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->->Cycle: ->->-> Pairs: ISPALLISTKIND(active(X)) -> ISPALLISTKIND(X) ISPALLISTKIND(mark(X)) -> ISPALLISTKIND(X) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->->Cycle: ->->-> Pairs: ISPAL(active(X)) -> ISPAL(X) ISPAL(mark(X)) -> ISPAL(X) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->->Cycle: ->->-> Pairs: ISNEPAL(active(X)) -> ISNEPAL(X) ISNEPAL(mark(X)) -> ISNEPAL(X) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->->Cycle: ->->-> Pairs: ISNELIST(active(X)) -> ISNELIST(X) ISNELIST(mark(X)) -> ISNELIST(X) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->->Cycle: ->->-> Pairs: ISLIST(active(X)) -> ISLIST(X) ISLIST(mark(X)) -> ISLIST(X) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->->Cycle: ->->-> Pairs: __#(active(X1),X2) -> __#(X1,X2) __#(mark(X1),X2) -> __#(X1,X2) __#(X1,active(X2)) -> __#(X1,X2) __#(X1,mark(X2)) -> __#(X1,X2) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->->Cycle: ->->-> Pairs: U92#(active(X)) -> U92#(X) U92#(mark(X)) -> U92#(X) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->->Cycle: ->->-> Pairs: U91#(active(X1),X2) -> U91#(X1,X2) U91#(mark(X1),X2) -> U91#(X1,X2) U91#(X1,active(X2)) -> U91#(X1,X2) U91#(X1,mark(X2)) -> U91#(X1,X2) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->->Cycle: ->->-> Pairs: U83#(active(X)) -> U83#(X) U83#(mark(X)) -> U83#(X) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->->Cycle: ->->-> Pairs: U82#(active(X1),X2) -> U82#(X1,X2) U82#(mark(X1),X2) -> U82#(X1,X2) U82#(X1,active(X2)) -> U82#(X1,X2) U82#(X1,mark(X2)) -> U82#(X1,X2) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->->Cycle: ->->-> Pairs: U81#(active(X1),X2) -> U81#(X1,X2) U81#(mark(X1),X2) -> U81#(X1,X2) U81#(X1,active(X2)) -> U81#(X1,X2) U81#(X1,mark(X2)) -> U81#(X1,X2) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->->Cycle: ->->-> Pairs: U74#(active(X)) -> U74#(X) U74#(mark(X)) -> U74#(X) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->->Cycle: ->->-> Pairs: U73#(active(X1),X2) -> U73#(X1,X2) U73#(mark(X1),X2) -> U73#(X1,X2) U73#(X1,active(X2)) -> U73#(X1,X2) U73#(X1,mark(X2)) -> U73#(X1,X2) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->->Cycle: ->->-> Pairs: U72#(active(X1),X2) -> U72#(X1,X2) U72#(mark(X1),X2) -> U72#(X1,X2) U72#(X1,active(X2)) -> U72#(X1,X2) U72#(X1,mark(X2)) -> U72#(X1,X2) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->->Cycle: ->->-> Pairs: U71#(active(X1),X2,X3) -> U71#(X1,X2,X3) U71#(mark(X1),X2,X3) -> U71#(X1,X2,X3) U71#(X1,active(X2),X3) -> U71#(X1,X2,X3) U71#(X1,mark(X2),X3) -> U71#(X1,X2,X3) U71#(X1,X2,active(X3)) -> U71#(X1,X2,X3) U71#(X1,X2,mark(X3)) -> U71#(X1,X2,X3) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->->Cycle: ->->-> Pairs: U63#(active(X)) -> U63#(X) U63#(mark(X)) -> U63#(X) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->->Cycle: ->->-> Pairs: U62#(active(X1),X2) -> U62#(X1,X2) U62#(mark(X1),X2) -> U62#(X1,X2) U62#(X1,active(X2)) -> U62#(X1,X2) U62#(X1,mark(X2)) -> U62#(X1,X2) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->->Cycle: ->->-> Pairs: U61#(active(X1),X2) -> U61#(X1,X2) U61#(mark(X1),X2) -> U61#(X1,X2) U61#(X1,active(X2)) -> U61#(X1,X2) U61#(X1,mark(X2)) -> U61#(X1,X2) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->->Cycle: ->->-> Pairs: U56#(active(X)) -> U56#(X) U56#(mark(X)) -> U56#(X) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->->Cycle: ->->-> Pairs: U55#(active(X1),X2) -> U55#(X1,X2) U55#(mark(X1),X2) -> U55#(X1,X2) U55#(X1,active(X2)) -> U55#(X1,X2) U55#(X1,mark(X2)) -> U55#(X1,X2) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->->Cycle: ->->-> Pairs: U54#(active(X1),X2,X3) -> U54#(X1,X2,X3) U54#(mark(X1),X2,X3) -> U54#(X1,X2,X3) U54#(X1,active(X2),X3) -> U54#(X1,X2,X3) U54#(X1,mark(X2),X3) -> U54#(X1,X2,X3) U54#(X1,X2,active(X3)) -> U54#(X1,X2,X3) U54#(X1,X2,mark(X3)) -> U54#(X1,X2,X3) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->->Cycle: ->->-> Pairs: U53#(active(X1),X2,X3) -> U53#(X1,X2,X3) U53#(mark(X1),X2,X3) -> U53#(X1,X2,X3) U53#(X1,active(X2),X3) -> U53#(X1,X2,X3) U53#(X1,mark(X2),X3) -> U53#(X1,X2,X3) U53#(X1,X2,active(X3)) -> U53#(X1,X2,X3) U53#(X1,X2,mark(X3)) -> U53#(X1,X2,X3) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->->Cycle: ->->-> Pairs: U52#(active(X1),X2,X3) -> U52#(X1,X2,X3) U52#(mark(X1),X2,X3) -> U52#(X1,X2,X3) U52#(X1,active(X2),X3) -> U52#(X1,X2,X3) U52#(X1,mark(X2),X3) -> U52#(X1,X2,X3) U52#(X1,X2,active(X3)) -> U52#(X1,X2,X3) U52#(X1,X2,mark(X3)) -> U52#(X1,X2,X3) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->->Cycle: ->->-> Pairs: U51#(active(X1),X2,X3) -> U51#(X1,X2,X3) U51#(mark(X1),X2,X3) -> U51#(X1,X2,X3) U51#(X1,active(X2),X3) -> U51#(X1,X2,X3) U51#(X1,mark(X2),X3) -> U51#(X1,X2,X3) U51#(X1,X2,active(X3)) -> U51#(X1,X2,X3) U51#(X1,X2,mark(X3)) -> U51#(X1,X2,X3) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->->Cycle: ->->-> Pairs: U46#(active(X)) -> U46#(X) U46#(mark(X)) -> U46#(X) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->->Cycle: ->->-> Pairs: U45#(active(X1),X2) -> U45#(X1,X2) U45#(mark(X1),X2) -> U45#(X1,X2) U45#(X1,active(X2)) -> U45#(X1,X2) U45#(X1,mark(X2)) -> U45#(X1,X2) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->->Cycle: ->->-> Pairs: U44#(active(X1),X2,X3) -> U44#(X1,X2,X3) U44#(mark(X1),X2,X3) -> U44#(X1,X2,X3) U44#(X1,active(X2),X3) -> U44#(X1,X2,X3) U44#(X1,mark(X2),X3) -> U44#(X1,X2,X3) U44#(X1,X2,active(X3)) -> U44#(X1,X2,X3) U44#(X1,X2,mark(X3)) -> U44#(X1,X2,X3) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->->Cycle: ->->-> Pairs: U43#(active(X1),X2,X3) -> U43#(X1,X2,X3) U43#(mark(X1),X2,X3) -> U43#(X1,X2,X3) U43#(X1,active(X2),X3) -> U43#(X1,X2,X3) U43#(X1,mark(X2),X3) -> U43#(X1,X2,X3) U43#(X1,X2,active(X3)) -> U43#(X1,X2,X3) U43#(X1,X2,mark(X3)) -> U43#(X1,X2,X3) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->->Cycle: ->->-> Pairs: U42#(active(X1),X2,X3) -> U42#(X1,X2,X3) U42#(mark(X1),X2,X3) -> U42#(X1,X2,X3) U42#(X1,active(X2),X3) -> U42#(X1,X2,X3) U42#(X1,mark(X2),X3) -> U42#(X1,X2,X3) U42#(X1,X2,active(X3)) -> U42#(X1,X2,X3) U42#(X1,X2,mark(X3)) -> U42#(X1,X2,X3) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->->Cycle: ->->-> Pairs: U41#(active(X1),X2,X3) -> U41#(X1,X2,X3) U41#(mark(X1),X2,X3) -> U41#(X1,X2,X3) U41#(X1,active(X2),X3) -> U41#(X1,X2,X3) U41#(X1,mark(X2),X3) -> U41#(X1,X2,X3) U41#(X1,X2,active(X3)) -> U41#(X1,X2,X3) U41#(X1,X2,mark(X3)) -> U41#(X1,X2,X3) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->->Cycle: ->->-> Pairs: U33#(active(X)) -> U33#(X) U33#(mark(X)) -> U33#(X) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->->Cycle: ->->-> Pairs: U32#(active(X1),X2) -> U32#(X1,X2) U32#(mark(X1),X2) -> U32#(X1,X2) U32#(X1,active(X2)) -> U32#(X1,X2) U32#(X1,mark(X2)) -> U32#(X1,X2) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->->Cycle: ->->-> Pairs: U31#(active(X1),X2) -> U31#(X1,X2) U31#(mark(X1),X2) -> U31#(X1,X2) U31#(X1,active(X2)) -> U31#(X1,X2) U31#(X1,mark(X2)) -> U31#(X1,X2) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->->Cycle: ->->-> Pairs: U26#(active(X)) -> U26#(X) U26#(mark(X)) -> U26#(X) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->->Cycle: ->->-> Pairs: U25#(active(X1),X2) -> U25#(X1,X2) U25#(mark(X1),X2) -> U25#(X1,X2) U25#(X1,active(X2)) -> U25#(X1,X2) U25#(X1,mark(X2)) -> U25#(X1,X2) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->->Cycle: ->->-> Pairs: U24#(active(X1),X2,X3) -> U24#(X1,X2,X3) U24#(mark(X1),X2,X3) -> U24#(X1,X2,X3) U24#(X1,active(X2),X3) -> U24#(X1,X2,X3) U24#(X1,mark(X2),X3) -> U24#(X1,X2,X3) U24#(X1,X2,active(X3)) -> U24#(X1,X2,X3) U24#(X1,X2,mark(X3)) -> U24#(X1,X2,X3) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->->Cycle: ->->-> Pairs: U23#(active(X1),X2,X3) -> U23#(X1,X2,X3) U23#(mark(X1),X2,X3) -> U23#(X1,X2,X3) U23#(X1,active(X2),X3) -> U23#(X1,X2,X3) U23#(X1,mark(X2),X3) -> U23#(X1,X2,X3) U23#(X1,X2,active(X3)) -> U23#(X1,X2,X3) U23#(X1,X2,mark(X3)) -> U23#(X1,X2,X3) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->->Cycle: ->->-> Pairs: U22#(active(X1),X2,X3) -> U22#(X1,X2,X3) U22#(mark(X1),X2,X3) -> U22#(X1,X2,X3) U22#(X1,active(X2),X3) -> U22#(X1,X2,X3) U22#(X1,mark(X2),X3) -> U22#(X1,X2,X3) U22#(X1,X2,active(X3)) -> U22#(X1,X2,X3) U22#(X1,X2,mark(X3)) -> U22#(X1,X2,X3) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->->Cycle: ->->-> Pairs: U21#(active(X1),X2,X3) -> U21#(X1,X2,X3) U21#(mark(X1),X2,X3) -> U21#(X1,X2,X3) U21#(X1,active(X2),X3) -> U21#(X1,X2,X3) U21#(X1,mark(X2),X3) -> U21#(X1,X2,X3) U21#(X1,X2,active(X3)) -> U21#(X1,X2,X3) U21#(X1,X2,mark(X3)) -> U21#(X1,X2,X3) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->->Cycle: ->->-> Pairs: U13#(active(X)) -> U13#(X) U13#(mark(X)) -> U13#(X) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->->Cycle: ->->-> Pairs: U12#(active(X1),X2) -> U12#(X1,X2) U12#(mark(X1),X2) -> U12#(X1,X2) U12#(X1,active(X2)) -> U12#(X1,X2) U12#(X1,mark(X2)) -> U12#(X1,X2) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->->Cycle: ->->-> Pairs: U11#(active(X1),X2) -> U11#(X1,X2) U11#(mark(X1),X2) -> U11#(X1,X2) U11#(X1,active(X2)) -> U11#(X1,X2) U11#(X1,mark(X2)) -> U11#(X1,X2) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->->Cycle: ->->-> Pairs: ACTIVE(U11(tt,V)) -> MARK(U12(isPalListKind(V),V)) ACTIVE(U12(tt,V)) -> MARK(U13(isNeList(V))) ACTIVE(U21(tt,V1,V2)) -> MARK(U22(isPalListKind(V1),V1,V2)) ACTIVE(U22(tt,V1,V2)) -> MARK(U23(isPalListKind(V2),V1,V2)) ACTIVE(U23(tt,V1,V2)) -> MARK(U24(isPalListKind(V2),V1,V2)) ACTIVE(U24(tt,V1,V2)) -> MARK(U25(isList(V1),V2)) ACTIVE(U25(tt,V2)) -> MARK(U26(isList(V2))) ACTIVE(U31(tt,V)) -> MARK(U32(isPalListKind(V),V)) ACTIVE(U32(tt,V)) -> MARK(U33(isQid(V))) ACTIVE(U41(tt,V1,V2)) -> MARK(U42(isPalListKind(V1),V1,V2)) ACTIVE(U42(tt,V1,V2)) -> MARK(U43(isPalListKind(V2),V1,V2)) ACTIVE(U43(tt,V1,V2)) -> MARK(U44(isPalListKind(V2),V1,V2)) ACTIVE(U44(tt,V1,V2)) -> MARK(U45(isList(V1),V2)) ACTIVE(U45(tt,V2)) -> MARK(U46(isNeList(V2))) ACTIVE(U51(tt,V1,V2)) -> MARK(U52(isPalListKind(V1),V1,V2)) ACTIVE(U52(tt,V1,V2)) -> MARK(U53(isPalListKind(V2),V1,V2)) ACTIVE(U53(tt,V1,V2)) -> MARK(U54(isPalListKind(V2),V1,V2)) ACTIVE(U54(tt,V1,V2)) -> MARK(U55(isNeList(V1),V2)) ACTIVE(U55(tt,V2)) -> MARK(U56(isList(V2))) ACTIVE(U61(tt,V)) -> MARK(U62(isPalListKind(V),V)) ACTIVE(U62(tt,V)) -> MARK(U63(isQid(V))) ACTIVE(U71(tt,I,P)) -> MARK(U72(isPalListKind(I),P)) ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) The problem is decomposed in 44 subproblems. Problem 1.1: Subterm Processor: -> Pairs: ISQID(active(X)) -> ISQID(X) ISQID(mark(X)) -> ISQID(X) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(ISQID) = 1 Problem 1.1: SCC Processor: -> Pairs: Empty -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.2: Subterm Processor: -> Pairs: ISPALLISTKIND(active(X)) -> ISPALLISTKIND(X) ISPALLISTKIND(mark(X)) -> ISPALLISTKIND(X) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(ISPALLISTKIND) = 1 Problem 1.2: SCC Processor: -> Pairs: Empty -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.3: Subterm Processor: -> Pairs: ISPAL(active(X)) -> ISPAL(X) ISPAL(mark(X)) -> ISPAL(X) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(ISPAL) = 1 Problem 1.3: SCC Processor: -> Pairs: Empty -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.4: Subterm Processor: -> Pairs: ISNEPAL(active(X)) -> ISNEPAL(X) ISNEPAL(mark(X)) -> ISNEPAL(X) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(ISNEPAL) = 1 Problem 1.4: SCC Processor: -> Pairs: Empty -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.5: Subterm Processor: -> Pairs: ISNELIST(active(X)) -> ISNELIST(X) ISNELIST(mark(X)) -> ISNELIST(X) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(ISNELIST) = 1 Problem 1.5: SCC Processor: -> Pairs: Empty -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.6: Subterm Processor: -> Pairs: ISLIST(active(X)) -> ISLIST(X) ISLIST(mark(X)) -> ISLIST(X) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(ISLIST) = 1 Problem 1.6: SCC Processor: -> Pairs: Empty -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.7: Subterm Processor: -> Pairs: __#(active(X1),X2) -> __#(X1,X2) __#(mark(X1),X2) -> __#(X1,X2) __#(X1,active(X2)) -> __#(X1,X2) __#(X1,mark(X2)) -> __#(X1,X2) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(__#) = 1 Problem 1.7: SCC Processor: -> Pairs: __#(X1,active(X2)) -> __#(X1,X2) __#(X1,mark(X2)) -> __#(X1,X2) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: __#(X1,active(X2)) -> __#(X1,X2) __#(X1,mark(X2)) -> __#(X1,X2) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.7: Subterm Processor: -> Pairs: __#(X1,active(X2)) -> __#(X1,X2) __#(X1,mark(X2)) -> __#(X1,X2) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(__#) = 2 Problem 1.7: SCC Processor: -> Pairs: Empty -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.8: Subterm Processor: -> Pairs: U92#(active(X)) -> U92#(X) U92#(mark(X)) -> U92#(X) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U92#) = 1 Problem 1.8: SCC Processor: -> Pairs: Empty -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.9: Subterm Processor: -> Pairs: U91#(active(X1),X2) -> U91#(X1,X2) U91#(mark(X1),X2) -> U91#(X1,X2) U91#(X1,active(X2)) -> U91#(X1,X2) U91#(X1,mark(X2)) -> U91#(X1,X2) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U91#) = 1 Problem 1.9: SCC Processor: -> Pairs: U91#(X1,active(X2)) -> U91#(X1,X2) U91#(X1,mark(X2)) -> U91#(X1,X2) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: U91#(X1,active(X2)) -> U91#(X1,X2) U91#(X1,mark(X2)) -> U91#(X1,X2) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.9: Subterm Processor: -> Pairs: U91#(X1,active(X2)) -> U91#(X1,X2) U91#(X1,mark(X2)) -> U91#(X1,X2) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U91#) = 2 Problem 1.9: SCC Processor: -> Pairs: Empty -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.10: Subterm Processor: -> Pairs: U83#(active(X)) -> U83#(X) U83#(mark(X)) -> U83#(X) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U83#) = 1 Problem 1.10: SCC Processor: -> Pairs: Empty -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.11: Subterm Processor: -> Pairs: U82#(active(X1),X2) -> U82#(X1,X2) U82#(mark(X1),X2) -> U82#(X1,X2) U82#(X1,active(X2)) -> U82#(X1,X2) U82#(X1,mark(X2)) -> U82#(X1,X2) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U82#) = 1 Problem 1.11: SCC Processor: -> Pairs: U82#(X1,active(X2)) -> U82#(X1,X2) U82#(X1,mark(X2)) -> U82#(X1,X2) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: U82#(X1,active(X2)) -> U82#(X1,X2) U82#(X1,mark(X2)) -> U82#(X1,X2) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.11: Subterm Processor: -> Pairs: U82#(X1,active(X2)) -> U82#(X1,X2) U82#(X1,mark(X2)) -> U82#(X1,X2) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U82#) = 2 Problem 1.11: SCC Processor: -> Pairs: Empty -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.12: Subterm Processor: -> Pairs: U81#(active(X1),X2) -> U81#(X1,X2) U81#(mark(X1),X2) -> U81#(X1,X2) U81#(X1,active(X2)) -> U81#(X1,X2) U81#(X1,mark(X2)) -> U81#(X1,X2) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U81#) = 1 Problem 1.12: SCC Processor: -> Pairs: U81#(X1,active(X2)) -> U81#(X1,X2) U81#(X1,mark(X2)) -> U81#(X1,X2) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: U81#(X1,active(X2)) -> U81#(X1,X2) U81#(X1,mark(X2)) -> U81#(X1,X2) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.12: Subterm Processor: -> Pairs: U81#(X1,active(X2)) -> U81#(X1,X2) U81#(X1,mark(X2)) -> U81#(X1,X2) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U81#) = 2 Problem 1.12: SCC Processor: -> Pairs: Empty -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.13: Subterm Processor: -> Pairs: U74#(active(X)) -> U74#(X) U74#(mark(X)) -> U74#(X) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U74#) = 1 Problem 1.13: SCC Processor: -> Pairs: Empty -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.14: Subterm Processor: -> Pairs: U73#(active(X1),X2) -> U73#(X1,X2) U73#(mark(X1),X2) -> U73#(X1,X2) U73#(X1,active(X2)) -> U73#(X1,X2) U73#(X1,mark(X2)) -> U73#(X1,X2) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U73#) = 1 Problem 1.14: SCC Processor: -> Pairs: U73#(X1,active(X2)) -> U73#(X1,X2) U73#(X1,mark(X2)) -> U73#(X1,X2) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: U73#(X1,active(X2)) -> U73#(X1,X2) U73#(X1,mark(X2)) -> U73#(X1,X2) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.14: Subterm Processor: -> Pairs: U73#(X1,active(X2)) -> U73#(X1,X2) U73#(X1,mark(X2)) -> U73#(X1,X2) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U73#) = 2 Problem 1.14: SCC Processor: -> Pairs: Empty -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.15: Subterm Processor: -> Pairs: U72#(active(X1),X2) -> U72#(X1,X2) U72#(mark(X1),X2) -> U72#(X1,X2) U72#(X1,active(X2)) -> U72#(X1,X2) U72#(X1,mark(X2)) -> U72#(X1,X2) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U72#) = 1 Problem 1.15: SCC Processor: -> Pairs: U72#(X1,active(X2)) -> U72#(X1,X2) U72#(X1,mark(X2)) -> U72#(X1,X2) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: U72#(X1,active(X2)) -> U72#(X1,X2) U72#(X1,mark(X2)) -> U72#(X1,X2) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.15: Subterm Processor: -> Pairs: U72#(X1,active(X2)) -> U72#(X1,X2) U72#(X1,mark(X2)) -> U72#(X1,X2) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U72#) = 2 Problem 1.15: SCC Processor: -> Pairs: Empty -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.16: Subterm Processor: -> Pairs: U71#(active(X1),X2,X3) -> U71#(X1,X2,X3) U71#(mark(X1),X2,X3) -> U71#(X1,X2,X3) U71#(X1,active(X2),X3) -> U71#(X1,X2,X3) U71#(X1,mark(X2),X3) -> U71#(X1,X2,X3) U71#(X1,X2,active(X3)) -> U71#(X1,X2,X3) U71#(X1,X2,mark(X3)) -> U71#(X1,X2,X3) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U71#) = 1 Problem 1.16: SCC Processor: -> Pairs: U71#(X1,active(X2),X3) -> U71#(X1,X2,X3) U71#(X1,mark(X2),X3) -> U71#(X1,X2,X3) U71#(X1,X2,active(X3)) -> U71#(X1,X2,X3) U71#(X1,X2,mark(X3)) -> U71#(X1,X2,X3) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: U71#(X1,active(X2),X3) -> U71#(X1,X2,X3) U71#(X1,mark(X2),X3) -> U71#(X1,X2,X3) U71#(X1,X2,active(X3)) -> U71#(X1,X2,X3) U71#(X1,X2,mark(X3)) -> U71#(X1,X2,X3) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.16: Subterm Processor: -> Pairs: U71#(X1,active(X2),X3) -> U71#(X1,X2,X3) U71#(X1,mark(X2),X3) -> U71#(X1,X2,X3) U71#(X1,X2,active(X3)) -> U71#(X1,X2,X3) U71#(X1,X2,mark(X3)) -> U71#(X1,X2,X3) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U71#) = 2 Problem 1.16: SCC Processor: -> Pairs: U71#(X1,X2,active(X3)) -> U71#(X1,X2,X3) U71#(X1,X2,mark(X3)) -> U71#(X1,X2,X3) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: U71#(X1,X2,active(X3)) -> U71#(X1,X2,X3) U71#(X1,X2,mark(X3)) -> U71#(X1,X2,X3) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.16: Subterm Processor: -> Pairs: U71#(X1,X2,active(X3)) -> U71#(X1,X2,X3) U71#(X1,X2,mark(X3)) -> U71#(X1,X2,X3) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U71#) = 3 Problem 1.16: SCC Processor: -> Pairs: Empty -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.17: Subterm Processor: -> Pairs: U63#(active(X)) -> U63#(X) U63#(mark(X)) -> U63#(X) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U63#) = 1 Problem 1.17: SCC Processor: -> Pairs: Empty -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.18: Subterm Processor: -> Pairs: U62#(active(X1),X2) -> U62#(X1,X2) U62#(mark(X1),X2) -> U62#(X1,X2) U62#(X1,active(X2)) -> U62#(X1,X2) U62#(X1,mark(X2)) -> U62#(X1,X2) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U62#) = 1 Problem 1.18: SCC Processor: -> Pairs: U62#(X1,active(X2)) -> U62#(X1,X2) U62#(X1,mark(X2)) -> U62#(X1,X2) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: U62#(X1,active(X2)) -> U62#(X1,X2) U62#(X1,mark(X2)) -> U62#(X1,X2) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.18: Subterm Processor: -> Pairs: U62#(X1,active(X2)) -> U62#(X1,X2) U62#(X1,mark(X2)) -> U62#(X1,X2) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U62#) = 2 Problem 1.18: SCC Processor: -> Pairs: Empty -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.19: Subterm Processor: -> Pairs: U61#(active(X1),X2) -> U61#(X1,X2) U61#(mark(X1),X2) -> U61#(X1,X2) U61#(X1,active(X2)) -> U61#(X1,X2) U61#(X1,mark(X2)) -> U61#(X1,X2) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U61#) = 1 Problem 1.19: SCC Processor: -> Pairs: U61#(X1,active(X2)) -> U61#(X1,X2) U61#(X1,mark(X2)) -> U61#(X1,X2) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: U61#(X1,active(X2)) -> U61#(X1,X2) U61#(X1,mark(X2)) -> U61#(X1,X2) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.19: Subterm Processor: -> Pairs: U61#(X1,active(X2)) -> U61#(X1,X2) U61#(X1,mark(X2)) -> U61#(X1,X2) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U61#) = 2 Problem 1.19: SCC Processor: -> Pairs: Empty -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.20: Subterm Processor: -> Pairs: U56#(active(X)) -> U56#(X) U56#(mark(X)) -> U56#(X) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U56#) = 1 Problem 1.20: SCC Processor: -> Pairs: Empty -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.21: Subterm Processor: -> Pairs: U55#(active(X1),X2) -> U55#(X1,X2) U55#(mark(X1),X2) -> U55#(X1,X2) U55#(X1,active(X2)) -> U55#(X1,X2) U55#(X1,mark(X2)) -> U55#(X1,X2) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U55#) = 1 Problem 1.21: SCC Processor: -> Pairs: U55#(X1,active(X2)) -> U55#(X1,X2) U55#(X1,mark(X2)) -> U55#(X1,X2) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: U55#(X1,active(X2)) -> U55#(X1,X2) U55#(X1,mark(X2)) -> U55#(X1,X2) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.21: Subterm Processor: -> Pairs: U55#(X1,active(X2)) -> U55#(X1,X2) U55#(X1,mark(X2)) -> U55#(X1,X2) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U55#) = 2 Problem 1.21: SCC Processor: -> Pairs: Empty -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.22: Subterm Processor: -> Pairs: U54#(active(X1),X2,X3) -> U54#(X1,X2,X3) U54#(mark(X1),X2,X3) -> U54#(X1,X2,X3) U54#(X1,active(X2),X3) -> U54#(X1,X2,X3) U54#(X1,mark(X2),X3) -> U54#(X1,X2,X3) U54#(X1,X2,active(X3)) -> U54#(X1,X2,X3) U54#(X1,X2,mark(X3)) -> U54#(X1,X2,X3) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U54#) = 1 Problem 1.22: SCC Processor: -> Pairs: U54#(X1,active(X2),X3) -> U54#(X1,X2,X3) U54#(X1,mark(X2),X3) -> U54#(X1,X2,X3) U54#(X1,X2,active(X3)) -> U54#(X1,X2,X3) U54#(X1,X2,mark(X3)) -> U54#(X1,X2,X3) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: U54#(X1,active(X2),X3) -> U54#(X1,X2,X3) U54#(X1,mark(X2),X3) -> U54#(X1,X2,X3) U54#(X1,X2,active(X3)) -> U54#(X1,X2,X3) U54#(X1,X2,mark(X3)) -> U54#(X1,X2,X3) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.22: Subterm Processor: -> Pairs: U54#(X1,active(X2),X3) -> U54#(X1,X2,X3) U54#(X1,mark(X2),X3) -> U54#(X1,X2,X3) U54#(X1,X2,active(X3)) -> U54#(X1,X2,X3) U54#(X1,X2,mark(X3)) -> U54#(X1,X2,X3) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U54#) = 2 Problem 1.22: SCC Processor: -> Pairs: U54#(X1,X2,active(X3)) -> U54#(X1,X2,X3) U54#(X1,X2,mark(X3)) -> U54#(X1,X2,X3) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: U54#(X1,X2,active(X3)) -> U54#(X1,X2,X3) U54#(X1,X2,mark(X3)) -> U54#(X1,X2,X3) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.22: Subterm Processor: -> Pairs: U54#(X1,X2,active(X3)) -> U54#(X1,X2,X3) U54#(X1,X2,mark(X3)) -> U54#(X1,X2,X3) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U54#) = 3 Problem 1.22: SCC Processor: -> Pairs: Empty -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.23: Subterm Processor: -> Pairs: U53#(active(X1),X2,X3) -> U53#(X1,X2,X3) U53#(mark(X1),X2,X3) -> U53#(X1,X2,X3) U53#(X1,active(X2),X3) -> U53#(X1,X2,X3) U53#(X1,mark(X2),X3) -> U53#(X1,X2,X3) U53#(X1,X2,active(X3)) -> U53#(X1,X2,X3) U53#(X1,X2,mark(X3)) -> U53#(X1,X2,X3) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U53#) = 1 Problem 1.23: SCC Processor: -> Pairs: U53#(X1,active(X2),X3) -> U53#(X1,X2,X3) U53#(X1,mark(X2),X3) -> U53#(X1,X2,X3) U53#(X1,X2,active(X3)) -> U53#(X1,X2,X3) U53#(X1,X2,mark(X3)) -> U53#(X1,X2,X3) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: U53#(X1,active(X2),X3) -> U53#(X1,X2,X3) U53#(X1,mark(X2),X3) -> U53#(X1,X2,X3) U53#(X1,X2,active(X3)) -> U53#(X1,X2,X3) U53#(X1,X2,mark(X3)) -> U53#(X1,X2,X3) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.23: Subterm Processor: -> Pairs: U53#(X1,active(X2),X3) -> U53#(X1,X2,X3) U53#(X1,mark(X2),X3) -> U53#(X1,X2,X3) U53#(X1,X2,active(X3)) -> U53#(X1,X2,X3) U53#(X1,X2,mark(X3)) -> U53#(X1,X2,X3) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U53#) = 2 Problem 1.23: SCC Processor: -> Pairs: U53#(X1,X2,active(X3)) -> U53#(X1,X2,X3) U53#(X1,X2,mark(X3)) -> U53#(X1,X2,X3) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: U53#(X1,X2,active(X3)) -> U53#(X1,X2,X3) U53#(X1,X2,mark(X3)) -> U53#(X1,X2,X3) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.23: Subterm Processor: -> Pairs: U53#(X1,X2,active(X3)) -> U53#(X1,X2,X3) U53#(X1,X2,mark(X3)) -> U53#(X1,X2,X3) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U53#) = 3 Problem 1.23: SCC Processor: -> Pairs: Empty -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.24: Subterm Processor: -> Pairs: U52#(active(X1),X2,X3) -> U52#(X1,X2,X3) U52#(mark(X1),X2,X3) -> U52#(X1,X2,X3) U52#(X1,active(X2),X3) -> U52#(X1,X2,X3) U52#(X1,mark(X2),X3) -> U52#(X1,X2,X3) U52#(X1,X2,active(X3)) -> U52#(X1,X2,X3) U52#(X1,X2,mark(X3)) -> U52#(X1,X2,X3) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U52#) = 1 Problem 1.24: SCC Processor: -> Pairs: U52#(X1,active(X2),X3) -> U52#(X1,X2,X3) U52#(X1,mark(X2),X3) -> U52#(X1,X2,X3) U52#(X1,X2,active(X3)) -> U52#(X1,X2,X3) U52#(X1,X2,mark(X3)) -> U52#(X1,X2,X3) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: U52#(X1,active(X2),X3) -> U52#(X1,X2,X3) U52#(X1,mark(X2),X3) -> U52#(X1,X2,X3) U52#(X1,X2,active(X3)) -> U52#(X1,X2,X3) U52#(X1,X2,mark(X3)) -> U52#(X1,X2,X3) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.24: Subterm Processor: -> Pairs: U52#(X1,active(X2),X3) -> U52#(X1,X2,X3) U52#(X1,mark(X2),X3) -> U52#(X1,X2,X3) U52#(X1,X2,active(X3)) -> U52#(X1,X2,X3) U52#(X1,X2,mark(X3)) -> U52#(X1,X2,X3) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U52#) = 2 Problem 1.24: SCC Processor: -> Pairs: U52#(X1,X2,active(X3)) -> U52#(X1,X2,X3) U52#(X1,X2,mark(X3)) -> U52#(X1,X2,X3) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: U52#(X1,X2,active(X3)) -> U52#(X1,X2,X3) U52#(X1,X2,mark(X3)) -> U52#(X1,X2,X3) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.24: Subterm Processor: -> Pairs: U52#(X1,X2,active(X3)) -> U52#(X1,X2,X3) U52#(X1,X2,mark(X3)) -> U52#(X1,X2,X3) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U52#) = 3 Problem 1.24: SCC Processor: -> Pairs: Empty -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.25: Subterm Processor: -> Pairs: U51#(active(X1),X2,X3) -> U51#(X1,X2,X3) U51#(mark(X1),X2,X3) -> U51#(X1,X2,X3) U51#(X1,active(X2),X3) -> U51#(X1,X2,X3) U51#(X1,mark(X2),X3) -> U51#(X1,X2,X3) U51#(X1,X2,active(X3)) -> U51#(X1,X2,X3) U51#(X1,X2,mark(X3)) -> U51#(X1,X2,X3) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U51#) = 1 Problem 1.25: SCC Processor: -> Pairs: U51#(X1,active(X2),X3) -> U51#(X1,X2,X3) U51#(X1,mark(X2),X3) -> U51#(X1,X2,X3) U51#(X1,X2,active(X3)) -> U51#(X1,X2,X3) U51#(X1,X2,mark(X3)) -> U51#(X1,X2,X3) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: U51#(X1,active(X2),X3) -> U51#(X1,X2,X3) U51#(X1,mark(X2),X3) -> U51#(X1,X2,X3) U51#(X1,X2,active(X3)) -> U51#(X1,X2,X3) U51#(X1,X2,mark(X3)) -> U51#(X1,X2,X3) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.25: Subterm Processor: -> Pairs: U51#(X1,active(X2),X3) -> U51#(X1,X2,X3) U51#(X1,mark(X2),X3) -> U51#(X1,X2,X3) U51#(X1,X2,active(X3)) -> U51#(X1,X2,X3) U51#(X1,X2,mark(X3)) -> U51#(X1,X2,X3) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U51#) = 2 Problem 1.25: SCC Processor: -> Pairs: U51#(X1,X2,active(X3)) -> U51#(X1,X2,X3) U51#(X1,X2,mark(X3)) -> U51#(X1,X2,X3) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: U51#(X1,X2,active(X3)) -> U51#(X1,X2,X3) U51#(X1,X2,mark(X3)) -> U51#(X1,X2,X3) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.25: Subterm Processor: -> Pairs: U51#(X1,X2,active(X3)) -> U51#(X1,X2,X3) U51#(X1,X2,mark(X3)) -> U51#(X1,X2,X3) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U51#) = 3 Problem 1.25: SCC Processor: -> Pairs: Empty -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.26: Subterm Processor: -> Pairs: U46#(active(X)) -> U46#(X) U46#(mark(X)) -> U46#(X) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U46#) = 1 Problem 1.26: SCC Processor: -> Pairs: Empty -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.27: Subterm Processor: -> Pairs: U45#(active(X1),X2) -> U45#(X1,X2) U45#(mark(X1),X2) -> U45#(X1,X2) U45#(X1,active(X2)) -> U45#(X1,X2) U45#(X1,mark(X2)) -> U45#(X1,X2) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U45#) = 1 Problem 1.27: SCC Processor: -> Pairs: U45#(X1,active(X2)) -> U45#(X1,X2) U45#(X1,mark(X2)) -> U45#(X1,X2) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: U45#(X1,active(X2)) -> U45#(X1,X2) U45#(X1,mark(X2)) -> U45#(X1,X2) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.27: Subterm Processor: -> Pairs: U45#(X1,active(X2)) -> U45#(X1,X2) U45#(X1,mark(X2)) -> U45#(X1,X2) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U45#) = 2 Problem 1.27: SCC Processor: -> Pairs: Empty -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.28: Subterm Processor: -> Pairs: U44#(active(X1),X2,X3) -> U44#(X1,X2,X3) U44#(mark(X1),X2,X3) -> U44#(X1,X2,X3) U44#(X1,active(X2),X3) -> U44#(X1,X2,X3) U44#(X1,mark(X2),X3) -> U44#(X1,X2,X3) U44#(X1,X2,active(X3)) -> U44#(X1,X2,X3) U44#(X1,X2,mark(X3)) -> U44#(X1,X2,X3) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U44#) = 1 Problem 1.28: SCC Processor: -> Pairs: U44#(X1,active(X2),X3) -> U44#(X1,X2,X3) U44#(X1,mark(X2),X3) -> U44#(X1,X2,X3) U44#(X1,X2,active(X3)) -> U44#(X1,X2,X3) U44#(X1,X2,mark(X3)) -> U44#(X1,X2,X3) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: U44#(X1,active(X2),X3) -> U44#(X1,X2,X3) U44#(X1,mark(X2),X3) -> U44#(X1,X2,X3) U44#(X1,X2,active(X3)) -> U44#(X1,X2,X3) U44#(X1,X2,mark(X3)) -> U44#(X1,X2,X3) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.28: Subterm Processor: -> Pairs: U44#(X1,active(X2),X3) -> U44#(X1,X2,X3) U44#(X1,mark(X2),X3) -> U44#(X1,X2,X3) U44#(X1,X2,active(X3)) -> U44#(X1,X2,X3) U44#(X1,X2,mark(X3)) -> U44#(X1,X2,X3) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U44#) = 2 Problem 1.28: SCC Processor: -> Pairs: U44#(X1,X2,active(X3)) -> U44#(X1,X2,X3) U44#(X1,X2,mark(X3)) -> U44#(X1,X2,X3) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: U44#(X1,X2,active(X3)) -> U44#(X1,X2,X3) U44#(X1,X2,mark(X3)) -> U44#(X1,X2,X3) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.28: Subterm Processor: -> Pairs: U44#(X1,X2,active(X3)) -> U44#(X1,X2,X3) U44#(X1,X2,mark(X3)) -> U44#(X1,X2,X3) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U44#) = 3 Problem 1.28: SCC Processor: -> Pairs: Empty -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.29: Subterm Processor: -> Pairs: U43#(active(X1),X2,X3) -> U43#(X1,X2,X3) U43#(mark(X1),X2,X3) -> U43#(X1,X2,X3) U43#(X1,active(X2),X3) -> U43#(X1,X2,X3) U43#(X1,mark(X2),X3) -> U43#(X1,X2,X3) U43#(X1,X2,active(X3)) -> U43#(X1,X2,X3) U43#(X1,X2,mark(X3)) -> U43#(X1,X2,X3) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U43#) = 1 Problem 1.29: SCC Processor: -> Pairs: U43#(X1,active(X2),X3) -> U43#(X1,X2,X3) U43#(X1,mark(X2),X3) -> U43#(X1,X2,X3) U43#(X1,X2,active(X3)) -> U43#(X1,X2,X3) U43#(X1,X2,mark(X3)) -> U43#(X1,X2,X3) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: U43#(X1,active(X2),X3) -> U43#(X1,X2,X3) U43#(X1,mark(X2),X3) -> U43#(X1,X2,X3) U43#(X1,X2,active(X3)) -> U43#(X1,X2,X3) U43#(X1,X2,mark(X3)) -> U43#(X1,X2,X3) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.29: Subterm Processor: -> Pairs: U43#(X1,active(X2),X3) -> U43#(X1,X2,X3) U43#(X1,mark(X2),X3) -> U43#(X1,X2,X3) U43#(X1,X2,active(X3)) -> U43#(X1,X2,X3) U43#(X1,X2,mark(X3)) -> U43#(X1,X2,X3) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U43#) = 2 Problem 1.29: SCC Processor: -> Pairs: U43#(X1,X2,active(X3)) -> U43#(X1,X2,X3) U43#(X1,X2,mark(X3)) -> U43#(X1,X2,X3) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: U43#(X1,X2,active(X3)) -> U43#(X1,X2,X3) U43#(X1,X2,mark(X3)) -> U43#(X1,X2,X3) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.29: Subterm Processor: -> Pairs: U43#(X1,X2,active(X3)) -> U43#(X1,X2,X3) U43#(X1,X2,mark(X3)) -> U43#(X1,X2,X3) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U43#) = 3 Problem 1.29: SCC Processor: -> Pairs: Empty -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.30: Subterm Processor: -> Pairs: U42#(active(X1),X2,X3) -> U42#(X1,X2,X3) U42#(mark(X1),X2,X3) -> U42#(X1,X2,X3) U42#(X1,active(X2),X3) -> U42#(X1,X2,X3) U42#(X1,mark(X2),X3) -> U42#(X1,X2,X3) U42#(X1,X2,active(X3)) -> U42#(X1,X2,X3) U42#(X1,X2,mark(X3)) -> U42#(X1,X2,X3) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U42#) = 1 Problem 1.30: SCC Processor: -> Pairs: U42#(X1,active(X2),X3) -> U42#(X1,X2,X3) U42#(X1,mark(X2),X3) -> U42#(X1,X2,X3) U42#(X1,X2,active(X3)) -> U42#(X1,X2,X3) U42#(X1,X2,mark(X3)) -> U42#(X1,X2,X3) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: U42#(X1,active(X2),X3) -> U42#(X1,X2,X3) U42#(X1,mark(X2),X3) -> U42#(X1,X2,X3) U42#(X1,X2,active(X3)) -> U42#(X1,X2,X3) U42#(X1,X2,mark(X3)) -> U42#(X1,X2,X3) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.30: Subterm Processor: -> Pairs: U42#(X1,active(X2),X3) -> U42#(X1,X2,X3) U42#(X1,mark(X2),X3) -> U42#(X1,X2,X3) U42#(X1,X2,active(X3)) -> U42#(X1,X2,X3) U42#(X1,X2,mark(X3)) -> U42#(X1,X2,X3) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U42#) = 2 Problem 1.30: SCC Processor: -> Pairs: U42#(X1,X2,active(X3)) -> U42#(X1,X2,X3) U42#(X1,X2,mark(X3)) -> U42#(X1,X2,X3) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: U42#(X1,X2,active(X3)) -> U42#(X1,X2,X3) U42#(X1,X2,mark(X3)) -> U42#(X1,X2,X3) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.30: Subterm Processor: -> Pairs: U42#(X1,X2,active(X3)) -> U42#(X1,X2,X3) U42#(X1,X2,mark(X3)) -> U42#(X1,X2,X3) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U42#) = 3 Problem 1.30: SCC Processor: -> Pairs: Empty -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.31: Subterm Processor: -> Pairs: U41#(active(X1),X2,X3) -> U41#(X1,X2,X3) U41#(mark(X1),X2,X3) -> U41#(X1,X2,X3) U41#(X1,active(X2),X3) -> U41#(X1,X2,X3) U41#(X1,mark(X2),X3) -> U41#(X1,X2,X3) U41#(X1,X2,active(X3)) -> U41#(X1,X2,X3) U41#(X1,X2,mark(X3)) -> U41#(X1,X2,X3) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U41#) = 1 Problem 1.31: SCC Processor: -> Pairs: U41#(X1,active(X2),X3) -> U41#(X1,X2,X3) U41#(X1,mark(X2),X3) -> U41#(X1,X2,X3) U41#(X1,X2,active(X3)) -> U41#(X1,X2,X3) U41#(X1,X2,mark(X3)) -> U41#(X1,X2,X3) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: U41#(X1,active(X2),X3) -> U41#(X1,X2,X3) U41#(X1,mark(X2),X3) -> U41#(X1,X2,X3) U41#(X1,X2,active(X3)) -> U41#(X1,X2,X3) U41#(X1,X2,mark(X3)) -> U41#(X1,X2,X3) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.31: Subterm Processor: -> Pairs: U41#(X1,active(X2),X3) -> U41#(X1,X2,X3) U41#(X1,mark(X2),X3) -> U41#(X1,X2,X3) U41#(X1,X2,active(X3)) -> U41#(X1,X2,X3) U41#(X1,X2,mark(X3)) -> U41#(X1,X2,X3) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U41#) = 2 Problem 1.31: SCC Processor: -> Pairs: U41#(X1,X2,active(X3)) -> U41#(X1,X2,X3) U41#(X1,X2,mark(X3)) -> U41#(X1,X2,X3) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: U41#(X1,X2,active(X3)) -> U41#(X1,X2,X3) U41#(X1,X2,mark(X3)) -> U41#(X1,X2,X3) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.31: Subterm Processor: -> Pairs: U41#(X1,X2,active(X3)) -> U41#(X1,X2,X3) U41#(X1,X2,mark(X3)) -> U41#(X1,X2,X3) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U41#) = 3 Problem 1.31: SCC Processor: -> Pairs: Empty -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.32: Subterm Processor: -> Pairs: U33#(active(X)) -> U33#(X) U33#(mark(X)) -> U33#(X) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U33#) = 1 Problem 1.32: SCC Processor: -> Pairs: Empty -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.33: Subterm Processor: -> Pairs: U32#(active(X1),X2) -> U32#(X1,X2) U32#(mark(X1),X2) -> U32#(X1,X2) U32#(X1,active(X2)) -> U32#(X1,X2) U32#(X1,mark(X2)) -> U32#(X1,X2) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U32#) = 1 Problem 1.33: SCC Processor: -> Pairs: U32#(X1,active(X2)) -> U32#(X1,X2) U32#(X1,mark(X2)) -> U32#(X1,X2) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: U32#(X1,active(X2)) -> U32#(X1,X2) U32#(X1,mark(X2)) -> U32#(X1,X2) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.33: Subterm Processor: -> Pairs: U32#(X1,active(X2)) -> U32#(X1,X2) U32#(X1,mark(X2)) -> U32#(X1,X2) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U32#) = 2 Problem 1.33: SCC Processor: -> Pairs: Empty -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.34: Subterm Processor: -> Pairs: U31#(active(X1),X2) -> U31#(X1,X2) U31#(mark(X1),X2) -> U31#(X1,X2) U31#(X1,active(X2)) -> U31#(X1,X2) U31#(X1,mark(X2)) -> U31#(X1,X2) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U31#) = 1 Problem 1.34: SCC Processor: -> Pairs: U31#(X1,active(X2)) -> U31#(X1,X2) U31#(X1,mark(X2)) -> U31#(X1,X2) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: U31#(X1,active(X2)) -> U31#(X1,X2) U31#(X1,mark(X2)) -> U31#(X1,X2) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.34: Subterm Processor: -> Pairs: U31#(X1,active(X2)) -> U31#(X1,X2) U31#(X1,mark(X2)) -> U31#(X1,X2) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U31#) = 2 Problem 1.34: SCC Processor: -> Pairs: Empty -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.35: Subterm Processor: -> Pairs: U26#(active(X)) -> U26#(X) U26#(mark(X)) -> U26#(X) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U26#) = 1 Problem 1.35: SCC Processor: -> Pairs: Empty -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.36: Subterm Processor: -> Pairs: U25#(active(X1),X2) -> U25#(X1,X2) U25#(mark(X1),X2) -> U25#(X1,X2) U25#(X1,active(X2)) -> U25#(X1,X2) U25#(X1,mark(X2)) -> U25#(X1,X2) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U25#) = 1 Problem 1.36: SCC Processor: -> Pairs: U25#(X1,active(X2)) -> U25#(X1,X2) U25#(X1,mark(X2)) -> U25#(X1,X2) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: U25#(X1,active(X2)) -> U25#(X1,X2) U25#(X1,mark(X2)) -> U25#(X1,X2) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.36: Subterm Processor: -> Pairs: U25#(X1,active(X2)) -> U25#(X1,X2) U25#(X1,mark(X2)) -> U25#(X1,X2) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U25#) = 2 Problem 1.36: SCC Processor: -> Pairs: Empty -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.37: Subterm Processor: -> Pairs: U24#(active(X1),X2,X3) -> U24#(X1,X2,X3) U24#(mark(X1),X2,X3) -> U24#(X1,X2,X3) U24#(X1,active(X2),X3) -> U24#(X1,X2,X3) U24#(X1,mark(X2),X3) -> U24#(X1,X2,X3) U24#(X1,X2,active(X3)) -> U24#(X1,X2,X3) U24#(X1,X2,mark(X3)) -> U24#(X1,X2,X3) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U24#) = 1 Problem 1.37: SCC Processor: -> Pairs: U24#(X1,active(X2),X3) -> U24#(X1,X2,X3) U24#(X1,mark(X2),X3) -> U24#(X1,X2,X3) U24#(X1,X2,active(X3)) -> U24#(X1,X2,X3) U24#(X1,X2,mark(X3)) -> U24#(X1,X2,X3) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: U24#(X1,active(X2),X3) -> U24#(X1,X2,X3) U24#(X1,mark(X2),X3) -> U24#(X1,X2,X3) U24#(X1,X2,active(X3)) -> U24#(X1,X2,X3) U24#(X1,X2,mark(X3)) -> U24#(X1,X2,X3) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.37: Subterm Processor: -> Pairs: U24#(X1,active(X2),X3) -> U24#(X1,X2,X3) U24#(X1,mark(X2),X3) -> U24#(X1,X2,X3) U24#(X1,X2,active(X3)) -> U24#(X1,X2,X3) U24#(X1,X2,mark(X3)) -> U24#(X1,X2,X3) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U24#) = 2 Problem 1.37: SCC Processor: -> Pairs: U24#(X1,X2,active(X3)) -> U24#(X1,X2,X3) U24#(X1,X2,mark(X3)) -> U24#(X1,X2,X3) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: U24#(X1,X2,active(X3)) -> U24#(X1,X2,X3) U24#(X1,X2,mark(X3)) -> U24#(X1,X2,X3) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.37: Subterm Processor: -> Pairs: U24#(X1,X2,active(X3)) -> U24#(X1,X2,X3) U24#(X1,X2,mark(X3)) -> U24#(X1,X2,X3) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U24#) = 3 Problem 1.37: SCC Processor: -> Pairs: Empty -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.38: Subterm Processor: -> Pairs: U23#(active(X1),X2,X3) -> U23#(X1,X2,X3) U23#(mark(X1),X2,X3) -> U23#(X1,X2,X3) U23#(X1,active(X2),X3) -> U23#(X1,X2,X3) U23#(X1,mark(X2),X3) -> U23#(X1,X2,X3) U23#(X1,X2,active(X3)) -> U23#(X1,X2,X3) U23#(X1,X2,mark(X3)) -> U23#(X1,X2,X3) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U23#) = 1 Problem 1.38: SCC Processor: -> Pairs: U23#(X1,active(X2),X3) -> U23#(X1,X2,X3) U23#(X1,mark(X2),X3) -> U23#(X1,X2,X3) U23#(X1,X2,active(X3)) -> U23#(X1,X2,X3) U23#(X1,X2,mark(X3)) -> U23#(X1,X2,X3) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: U23#(X1,active(X2),X3) -> U23#(X1,X2,X3) U23#(X1,mark(X2),X3) -> U23#(X1,X2,X3) U23#(X1,X2,active(X3)) -> U23#(X1,X2,X3) U23#(X1,X2,mark(X3)) -> U23#(X1,X2,X3) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.38: Subterm Processor: -> Pairs: U23#(X1,active(X2),X3) -> U23#(X1,X2,X3) U23#(X1,mark(X2),X3) -> U23#(X1,X2,X3) U23#(X1,X2,active(X3)) -> U23#(X1,X2,X3) U23#(X1,X2,mark(X3)) -> U23#(X1,X2,X3) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U23#) = 2 Problem 1.38: SCC Processor: -> Pairs: U23#(X1,X2,active(X3)) -> U23#(X1,X2,X3) U23#(X1,X2,mark(X3)) -> U23#(X1,X2,X3) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: U23#(X1,X2,active(X3)) -> U23#(X1,X2,X3) U23#(X1,X2,mark(X3)) -> U23#(X1,X2,X3) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.38: Subterm Processor: -> Pairs: U23#(X1,X2,active(X3)) -> U23#(X1,X2,X3) U23#(X1,X2,mark(X3)) -> U23#(X1,X2,X3) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U23#) = 3 Problem 1.38: SCC Processor: -> Pairs: Empty -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.39: Subterm Processor: -> Pairs: U22#(active(X1),X2,X3) -> U22#(X1,X2,X3) U22#(mark(X1),X2,X3) -> U22#(X1,X2,X3) U22#(X1,active(X2),X3) -> U22#(X1,X2,X3) U22#(X1,mark(X2),X3) -> U22#(X1,X2,X3) U22#(X1,X2,active(X3)) -> U22#(X1,X2,X3) U22#(X1,X2,mark(X3)) -> U22#(X1,X2,X3) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U22#) = 1 Problem 1.39: SCC Processor: -> Pairs: U22#(X1,active(X2),X3) -> U22#(X1,X2,X3) U22#(X1,mark(X2),X3) -> U22#(X1,X2,X3) U22#(X1,X2,active(X3)) -> U22#(X1,X2,X3) U22#(X1,X2,mark(X3)) -> U22#(X1,X2,X3) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: U22#(X1,active(X2),X3) -> U22#(X1,X2,X3) U22#(X1,mark(X2),X3) -> U22#(X1,X2,X3) U22#(X1,X2,active(X3)) -> U22#(X1,X2,X3) U22#(X1,X2,mark(X3)) -> U22#(X1,X2,X3) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.39: Subterm Processor: -> Pairs: U22#(X1,active(X2),X3) -> U22#(X1,X2,X3) U22#(X1,mark(X2),X3) -> U22#(X1,X2,X3) U22#(X1,X2,active(X3)) -> U22#(X1,X2,X3) U22#(X1,X2,mark(X3)) -> U22#(X1,X2,X3) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U22#) = 2 Problem 1.39: SCC Processor: -> Pairs: U22#(X1,X2,active(X3)) -> U22#(X1,X2,X3) U22#(X1,X2,mark(X3)) -> U22#(X1,X2,X3) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: U22#(X1,X2,active(X3)) -> U22#(X1,X2,X3) U22#(X1,X2,mark(X3)) -> U22#(X1,X2,X3) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.39: Subterm Processor: -> Pairs: U22#(X1,X2,active(X3)) -> U22#(X1,X2,X3) U22#(X1,X2,mark(X3)) -> U22#(X1,X2,X3) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U22#) = 3 Problem 1.39: SCC Processor: -> Pairs: Empty -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.40: Subterm Processor: -> Pairs: U21#(active(X1),X2,X3) -> U21#(X1,X2,X3) U21#(mark(X1),X2,X3) -> U21#(X1,X2,X3) U21#(X1,active(X2),X3) -> U21#(X1,X2,X3) U21#(X1,mark(X2),X3) -> U21#(X1,X2,X3) U21#(X1,X2,active(X3)) -> U21#(X1,X2,X3) U21#(X1,X2,mark(X3)) -> U21#(X1,X2,X3) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U21#) = 1 Problem 1.40: SCC Processor: -> Pairs: U21#(X1,active(X2),X3) -> U21#(X1,X2,X3) U21#(X1,mark(X2),X3) -> U21#(X1,X2,X3) U21#(X1,X2,active(X3)) -> U21#(X1,X2,X3) U21#(X1,X2,mark(X3)) -> U21#(X1,X2,X3) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: U21#(X1,active(X2),X3) -> U21#(X1,X2,X3) U21#(X1,mark(X2),X3) -> U21#(X1,X2,X3) U21#(X1,X2,active(X3)) -> U21#(X1,X2,X3) U21#(X1,X2,mark(X3)) -> U21#(X1,X2,X3) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.40: Subterm Processor: -> Pairs: U21#(X1,active(X2),X3) -> U21#(X1,X2,X3) U21#(X1,mark(X2),X3) -> U21#(X1,X2,X3) U21#(X1,X2,active(X3)) -> U21#(X1,X2,X3) U21#(X1,X2,mark(X3)) -> U21#(X1,X2,X3) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U21#) = 2 Problem 1.40: SCC Processor: -> Pairs: U21#(X1,X2,active(X3)) -> U21#(X1,X2,X3) U21#(X1,X2,mark(X3)) -> U21#(X1,X2,X3) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: U21#(X1,X2,active(X3)) -> U21#(X1,X2,X3) U21#(X1,X2,mark(X3)) -> U21#(X1,X2,X3) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.40: Subterm Processor: -> Pairs: U21#(X1,X2,active(X3)) -> U21#(X1,X2,X3) U21#(X1,X2,mark(X3)) -> U21#(X1,X2,X3) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U21#) = 3 Problem 1.40: SCC Processor: -> Pairs: Empty -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.41: Subterm Processor: -> Pairs: U13#(active(X)) -> U13#(X) U13#(mark(X)) -> U13#(X) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U13#) = 1 Problem 1.41: SCC Processor: -> Pairs: Empty -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.42: Subterm Processor: -> Pairs: U12#(active(X1),X2) -> U12#(X1,X2) U12#(mark(X1),X2) -> U12#(X1,X2) U12#(X1,active(X2)) -> U12#(X1,X2) U12#(X1,mark(X2)) -> U12#(X1,X2) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U12#) = 1 Problem 1.42: SCC Processor: -> Pairs: U12#(X1,active(X2)) -> U12#(X1,X2) U12#(X1,mark(X2)) -> U12#(X1,X2) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: U12#(X1,active(X2)) -> U12#(X1,X2) U12#(X1,mark(X2)) -> U12#(X1,X2) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.42: Subterm Processor: -> Pairs: U12#(X1,active(X2)) -> U12#(X1,X2) U12#(X1,mark(X2)) -> U12#(X1,X2) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U12#) = 2 Problem 1.42: SCC Processor: -> Pairs: Empty -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.43: Subterm Processor: -> Pairs: U11#(active(X1),X2) -> U11#(X1,X2) U11#(mark(X1),X2) -> U11#(X1,X2) U11#(X1,active(X2)) -> U11#(X1,X2) U11#(X1,mark(X2)) -> U11#(X1,X2) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U11#) = 1 Problem 1.43: SCC Processor: -> Pairs: U11#(X1,active(X2)) -> U11#(X1,X2) U11#(X1,mark(X2)) -> U11#(X1,X2) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: U11#(X1,active(X2)) -> U11#(X1,X2) U11#(X1,mark(X2)) -> U11#(X1,X2) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.43: Subterm Processor: -> Pairs: U11#(X1,active(X2)) -> U11#(X1,X2) U11#(X1,mark(X2)) -> U11#(X1,X2) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(U11#) = 2 Problem 1.43: SCC Processor: -> Pairs: Empty -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U11(tt,V)) -> MARK(U12(isPalListKind(V),V)) ACTIVE(U12(tt,V)) -> MARK(U13(isNeList(V))) ACTIVE(U21(tt,V1,V2)) -> MARK(U22(isPalListKind(V1),V1,V2)) ACTIVE(U22(tt,V1,V2)) -> MARK(U23(isPalListKind(V2),V1,V2)) ACTIVE(U23(tt,V1,V2)) -> MARK(U24(isPalListKind(V2),V1,V2)) ACTIVE(U24(tt,V1,V2)) -> MARK(U25(isList(V1),V2)) ACTIVE(U25(tt,V2)) -> MARK(U26(isList(V2))) ACTIVE(U31(tt,V)) -> MARK(U32(isPalListKind(V),V)) ACTIVE(U32(tt,V)) -> MARK(U33(isQid(V))) ACTIVE(U41(tt,V1,V2)) -> MARK(U42(isPalListKind(V1),V1,V2)) ACTIVE(U42(tt,V1,V2)) -> MARK(U43(isPalListKind(V2),V1,V2)) ACTIVE(U43(tt,V1,V2)) -> MARK(U44(isPalListKind(V2),V1,V2)) ACTIVE(U44(tt,V1,V2)) -> MARK(U45(isList(V1),V2)) ACTIVE(U45(tt,V2)) -> MARK(U46(isNeList(V2))) ACTIVE(U51(tt,V1,V2)) -> MARK(U52(isPalListKind(V1),V1,V2)) ACTIVE(U52(tt,V1,V2)) -> MARK(U53(isPalListKind(V2),V1,V2)) ACTIVE(U53(tt,V1,V2)) -> MARK(U54(isPalListKind(V2),V1,V2)) ACTIVE(U54(tt,V1,V2)) -> MARK(U55(isNeList(V1),V2)) ACTIVE(U55(tt,V2)) -> MARK(U56(isList(V2))) ACTIVE(U61(tt,V)) -> MARK(U62(isPalListKind(V),V)) ACTIVE(U62(tt,V)) -> MARK(U63(isQid(V))) ACTIVE(U71(tt,I,P)) -> MARK(U72(isPalListKind(I),P)) ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = X1 + 2.X2 + 1 [U12](X1,X2) = X1 + 2.X2 [U13](X) = X [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U22](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U23](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U24](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U25](X1,X2) = X1 + 2.X2 + 2 [U26](X) = X + 1 [U31](X1,X2) = X1 + 2.X2 [U32](X1,X2) = X1 + 2.X2 [U33](X) = X [U41](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 1 [U43](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 1 [U44](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 1 [U45](X1,X2) = X1 + 2.X2 + 1 [U46](X) = X [U51](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U52](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 1 [U53](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U54](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U55](X1,X2) = X1 + 2.X2 + 2 [U56](X) = X + 1 [U61](X1,X2) = X1 + 2.X2 + 1 [U62](X1,X2) = 2.X1 + 2.X2 [U63](X) = 2.X [U71](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U72](X1,X2) = 2.X1 + 2.X2 + 2 [U73](X1,X2) = X1 + 2 [U74](X) = X + 1 [U81](X1,X2) = 2.X1 + 2.X2 [U82](X1,X2) = X1 + 2.X2 + 1 [U83](X) = X [U91](X1,X2) = X1 [U92](X) = X [__](X1,X2) = X1 + X2 + 2 [active](X) = X [isList](X) = 2.X + 2 [isNeList](X) = 2.X + 1 [isNePal](X) = 2.X + 2 [isPal](X) = 2.X + 2 [isPalListKind](X) = 1 [isQid](X) = 1 [mark](X) = X [a] = 2 [e] = 0 [i] = 2 [nil] = 0 [o] = 0 [tt] = 1 [u] = 0 [ACTIVE](X) = 2.X + 1 [MARK](X) = 2.X + 1 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U12(tt,V)) -> MARK(U13(isNeList(V))) ACTIVE(U21(tt,V1,V2)) -> MARK(U22(isPalListKind(V1),V1,V2)) ACTIVE(U22(tt,V1,V2)) -> MARK(U23(isPalListKind(V2),V1,V2)) ACTIVE(U23(tt,V1,V2)) -> MARK(U24(isPalListKind(V2),V1,V2)) ACTIVE(U24(tt,V1,V2)) -> MARK(U25(isList(V1),V2)) ACTIVE(U25(tt,V2)) -> MARK(U26(isList(V2))) ACTIVE(U31(tt,V)) -> MARK(U32(isPalListKind(V),V)) ACTIVE(U32(tt,V)) -> MARK(U33(isQid(V))) ACTIVE(U41(tt,V1,V2)) -> MARK(U42(isPalListKind(V1),V1,V2)) ACTIVE(U42(tt,V1,V2)) -> MARK(U43(isPalListKind(V2),V1,V2)) ACTIVE(U43(tt,V1,V2)) -> MARK(U44(isPalListKind(V2),V1,V2)) ACTIVE(U44(tt,V1,V2)) -> MARK(U45(isList(V1),V2)) ACTIVE(U45(tt,V2)) -> MARK(U46(isNeList(V2))) ACTIVE(U51(tt,V1,V2)) -> MARK(U52(isPalListKind(V1),V1,V2)) ACTIVE(U52(tt,V1,V2)) -> MARK(U53(isPalListKind(V2),V1,V2)) ACTIVE(U53(tt,V1,V2)) -> MARK(U54(isPalListKind(V2),V1,V2)) ACTIVE(U54(tt,V1,V2)) -> MARK(U55(isNeList(V1),V2)) ACTIVE(U55(tt,V2)) -> MARK(U56(isList(V2))) ACTIVE(U61(tt,V)) -> MARK(U62(isPalListKind(V),V)) ACTIVE(U62(tt,V)) -> MARK(U63(isQid(V))) ACTIVE(U71(tt,I,P)) -> MARK(U72(isPalListKind(I),P)) ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U12(tt,V)) -> MARK(U13(isNeList(V))) ACTIVE(U21(tt,V1,V2)) -> MARK(U22(isPalListKind(V1),V1,V2)) ACTIVE(U22(tt,V1,V2)) -> MARK(U23(isPalListKind(V2),V1,V2)) ACTIVE(U23(tt,V1,V2)) -> MARK(U24(isPalListKind(V2),V1,V2)) ACTIVE(U24(tt,V1,V2)) -> MARK(U25(isList(V1),V2)) ACTIVE(U25(tt,V2)) -> MARK(U26(isList(V2))) ACTIVE(U31(tt,V)) -> MARK(U32(isPalListKind(V),V)) ACTIVE(U32(tt,V)) -> MARK(U33(isQid(V))) ACTIVE(U41(tt,V1,V2)) -> MARK(U42(isPalListKind(V1),V1,V2)) ACTIVE(U42(tt,V1,V2)) -> MARK(U43(isPalListKind(V2),V1,V2)) ACTIVE(U43(tt,V1,V2)) -> MARK(U44(isPalListKind(V2),V1,V2)) ACTIVE(U44(tt,V1,V2)) -> MARK(U45(isList(V1),V2)) ACTIVE(U45(tt,V2)) -> MARK(U46(isNeList(V2))) ACTIVE(U51(tt,V1,V2)) -> MARK(U52(isPalListKind(V1),V1,V2)) ACTIVE(U52(tt,V1,V2)) -> MARK(U53(isPalListKind(V2),V1,V2)) ACTIVE(U53(tt,V1,V2)) -> MARK(U54(isPalListKind(V2),V1,V2)) ACTIVE(U54(tt,V1,V2)) -> MARK(U55(isNeList(V1),V2)) ACTIVE(U55(tt,V2)) -> MARK(U56(isList(V2))) ACTIVE(U61(tt,V)) -> MARK(U62(isPalListKind(V),V)) ACTIVE(U62(tt,V)) -> MARK(U63(isQid(V))) ACTIVE(U71(tt,I,P)) -> MARK(U72(isPalListKind(I),P)) ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U12(tt,V)) -> MARK(U13(isNeList(V))) ACTIVE(U21(tt,V1,V2)) -> MARK(U22(isPalListKind(V1),V1,V2)) ACTIVE(U22(tt,V1,V2)) -> MARK(U23(isPalListKind(V2),V1,V2)) ACTIVE(U23(tt,V1,V2)) -> MARK(U24(isPalListKind(V2),V1,V2)) ACTIVE(U24(tt,V1,V2)) -> MARK(U25(isList(V1),V2)) ACTIVE(U25(tt,V2)) -> MARK(U26(isList(V2))) ACTIVE(U31(tt,V)) -> MARK(U32(isPalListKind(V),V)) ACTIVE(U32(tt,V)) -> MARK(U33(isQid(V))) ACTIVE(U41(tt,V1,V2)) -> MARK(U42(isPalListKind(V1),V1,V2)) ACTIVE(U42(tt,V1,V2)) -> MARK(U43(isPalListKind(V2),V1,V2)) ACTIVE(U43(tt,V1,V2)) -> MARK(U44(isPalListKind(V2),V1,V2)) ACTIVE(U44(tt,V1,V2)) -> MARK(U45(isList(V1),V2)) ACTIVE(U45(tt,V2)) -> MARK(U46(isNeList(V2))) ACTIVE(U51(tt,V1,V2)) -> MARK(U52(isPalListKind(V1),V1,V2)) ACTIVE(U52(tt,V1,V2)) -> MARK(U53(isPalListKind(V2),V1,V2)) ACTIVE(U53(tt,V1,V2)) -> MARK(U54(isPalListKind(V2),V1,V2)) ACTIVE(U54(tt,V1,V2)) -> MARK(U55(isNeList(V1),V2)) ACTIVE(U55(tt,V2)) -> MARK(U56(isList(V2))) ACTIVE(U61(tt,V)) -> MARK(U62(isPalListKind(V),V)) ACTIVE(U62(tt,V)) -> MARK(U63(isQid(V))) ACTIVE(U71(tt,I,P)) -> MARK(U72(isPalListKind(I),P)) ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = 2.X1 + 2.X2 + 1 [U12](X1,X2) = 2.X1 + 2.X2 + 1 [U13](X) = X [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U22](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U23](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U24](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U25](X1,X2) = X1 + 2.X2 + 1 [U26](X) = X [U31](X1,X2) = 2.X1 + 2.X2 [U32](X1,X2) = 2.X1 + X2 [U33](X) = X [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U43](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U44](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U45](X1,X2) = X1 + 2.X2 + 1 [U46](X) = X [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U52](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U53](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U54](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U55](X1,X2) = X1 + 2.X2 + 2 [U56](X) = X + 1 [U61](X1,X2) = 2.X1 + 2.X2 + 2 [U62](X1,X2) = 2.X1 + 2.X2 + 2 [U63](X) = 2.X + 2 [U71](X1,X2,X3) = 2.X1 + X2 + 2.X3 + 2 [U72](X1,X2) = 2.X1 + 2.X2 + 2 [U73](X1,X2) = X1 [U74](X) = 2.X [U81](X1,X2) = 2.X1 + 2.X2 + 2 [U82](X1,X2) = 2.X1 + 2.X2 + 2 [U83](X) = X [U91](X1,X2) = 2.X1 [U92](X) = X [__](X1,X2) = 2.X1 + X2 + 2 [active](X) = X [isList](X) = 2.X + 1 [isNeList](X) = 2.X [isNePal](X) = 2.X + 2 [isPal](X) = 2.X + 2 [isPalListKind](X) = 0 [isQid](X) = X [mark](X) = X [a] = 2 [e] = 2 [i] = 0 [nil] = 2 [o] = 1 [tt] = 0 [u] = 2 [ACTIVE](X) = 2.X + 2 [MARK](X) = 2.X + 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U21(tt,V1,V2)) -> MARK(U22(isPalListKind(V1),V1,V2)) ACTIVE(U22(tt,V1,V2)) -> MARK(U23(isPalListKind(V2),V1,V2)) ACTIVE(U23(tt,V1,V2)) -> MARK(U24(isPalListKind(V2),V1,V2)) ACTIVE(U24(tt,V1,V2)) -> MARK(U25(isList(V1),V2)) ACTIVE(U25(tt,V2)) -> MARK(U26(isList(V2))) ACTIVE(U31(tt,V)) -> MARK(U32(isPalListKind(V),V)) ACTIVE(U32(tt,V)) -> MARK(U33(isQid(V))) ACTIVE(U41(tt,V1,V2)) -> MARK(U42(isPalListKind(V1),V1,V2)) ACTIVE(U42(tt,V1,V2)) -> MARK(U43(isPalListKind(V2),V1,V2)) ACTIVE(U43(tt,V1,V2)) -> MARK(U44(isPalListKind(V2),V1,V2)) ACTIVE(U44(tt,V1,V2)) -> MARK(U45(isList(V1),V2)) ACTIVE(U45(tt,V2)) -> MARK(U46(isNeList(V2))) ACTIVE(U51(tt,V1,V2)) -> MARK(U52(isPalListKind(V1),V1,V2)) ACTIVE(U52(tt,V1,V2)) -> MARK(U53(isPalListKind(V2),V1,V2)) ACTIVE(U53(tt,V1,V2)) -> MARK(U54(isPalListKind(V2),V1,V2)) ACTIVE(U54(tt,V1,V2)) -> MARK(U55(isNeList(V1),V2)) ACTIVE(U55(tt,V2)) -> MARK(U56(isList(V2))) ACTIVE(U61(tt,V)) -> MARK(U62(isPalListKind(V),V)) ACTIVE(U62(tt,V)) -> MARK(U63(isQid(V))) ACTIVE(U71(tt,I,P)) -> MARK(U72(isPalListKind(I),P)) ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U21(tt,V1,V2)) -> MARK(U22(isPalListKind(V1),V1,V2)) ACTIVE(U22(tt,V1,V2)) -> MARK(U23(isPalListKind(V2),V1,V2)) ACTIVE(U23(tt,V1,V2)) -> MARK(U24(isPalListKind(V2),V1,V2)) ACTIVE(U24(tt,V1,V2)) -> MARK(U25(isList(V1),V2)) ACTIVE(U25(tt,V2)) -> MARK(U26(isList(V2))) ACTIVE(U31(tt,V)) -> MARK(U32(isPalListKind(V),V)) ACTIVE(U32(tt,V)) -> MARK(U33(isQid(V))) ACTIVE(U41(tt,V1,V2)) -> MARK(U42(isPalListKind(V1),V1,V2)) ACTIVE(U42(tt,V1,V2)) -> MARK(U43(isPalListKind(V2),V1,V2)) ACTIVE(U43(tt,V1,V2)) -> MARK(U44(isPalListKind(V2),V1,V2)) ACTIVE(U44(tt,V1,V2)) -> MARK(U45(isList(V1),V2)) ACTIVE(U45(tt,V2)) -> MARK(U46(isNeList(V2))) ACTIVE(U51(tt,V1,V2)) -> MARK(U52(isPalListKind(V1),V1,V2)) ACTIVE(U52(tt,V1,V2)) -> MARK(U53(isPalListKind(V2),V1,V2)) ACTIVE(U53(tt,V1,V2)) -> MARK(U54(isPalListKind(V2),V1,V2)) ACTIVE(U54(tt,V1,V2)) -> MARK(U55(isNeList(V1),V2)) ACTIVE(U55(tt,V2)) -> MARK(U56(isList(V2))) ACTIVE(U61(tt,V)) -> MARK(U62(isPalListKind(V),V)) ACTIVE(U62(tt,V)) -> MARK(U63(isQid(V))) ACTIVE(U71(tt,I,P)) -> MARK(U72(isPalListKind(I),P)) ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U21(tt,V1,V2)) -> MARK(U22(isPalListKind(V1),V1,V2)) ACTIVE(U22(tt,V1,V2)) -> MARK(U23(isPalListKind(V2),V1,V2)) ACTIVE(U23(tt,V1,V2)) -> MARK(U24(isPalListKind(V2),V1,V2)) ACTIVE(U24(tt,V1,V2)) -> MARK(U25(isList(V1),V2)) ACTIVE(U25(tt,V2)) -> MARK(U26(isList(V2))) ACTIVE(U31(tt,V)) -> MARK(U32(isPalListKind(V),V)) ACTIVE(U32(tt,V)) -> MARK(U33(isQid(V))) ACTIVE(U41(tt,V1,V2)) -> MARK(U42(isPalListKind(V1),V1,V2)) ACTIVE(U42(tt,V1,V2)) -> MARK(U43(isPalListKind(V2),V1,V2)) ACTIVE(U43(tt,V1,V2)) -> MARK(U44(isPalListKind(V2),V1,V2)) ACTIVE(U44(tt,V1,V2)) -> MARK(U45(isList(V1),V2)) ACTIVE(U45(tt,V2)) -> MARK(U46(isNeList(V2))) ACTIVE(U51(tt,V1,V2)) -> MARK(U52(isPalListKind(V1),V1,V2)) ACTIVE(U52(tt,V1,V2)) -> MARK(U53(isPalListKind(V2),V1,V2)) ACTIVE(U53(tt,V1,V2)) -> MARK(U54(isPalListKind(V2),V1,V2)) ACTIVE(U54(tt,V1,V2)) -> MARK(U55(isNeList(V1),V2)) ACTIVE(U55(tt,V2)) -> MARK(U56(isList(V2))) ACTIVE(U61(tt,V)) -> MARK(U62(isPalListKind(V),V)) ACTIVE(U62(tt,V)) -> MARK(U63(isQid(V))) ACTIVE(U71(tt,I,P)) -> MARK(U72(isPalListKind(I),P)) ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = X1 + 2.X2 [U12](X1,X2) = X1 + 2.X2 [U13](X) = X [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U22](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 1 [U23](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U24](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U25](X1,X2) = X1 + 2.X2 + 2 [U26](X) = X + 2 [U31](X1,X2) = X1 + 2.X2 [U32](X1,X2) = X1 + 2.X2 [U33](X) = 2.X [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U43](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 1 [U44](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 1 [U45](X1,X2) = X1 + 2.X2 + 2 [U46](X) = X + 2 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U52](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U53](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U54](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U55](X1,X2) = X1 + 2.X2 + 2 [U56](X) = X + 2 [U61](X1,X2) = X1 + 2.X2 [U62](X1,X2) = X1 + 2.X2 [U63](X) = 2.X [U71](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U72](X1,X2) = 2.X1 + 2.X2 + 2 [U73](X1,X2) = X1 + 2 [U74](X) = 2.X [U81](X1,X2) = X1 + 2.X2 [U82](X1,X2) = X1 + 2.X2 [U83](X) = X [U91](X1,X2) = X1 [U92](X) = X [__](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 [isPalListKind](X) = 2 [isQid](X) = X + 1 [mark](X) = X [a] = 2 [e] = 1 [i] = 2 [nil] = 2 [o] = 2 [tt] = 2 [u] = 2 [ACTIVE](X) = 2.X + 2 [MARK](X) = 2.X + 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U22(tt,V1,V2)) -> MARK(U23(isPalListKind(V2),V1,V2)) ACTIVE(U23(tt,V1,V2)) -> MARK(U24(isPalListKind(V2),V1,V2)) ACTIVE(U24(tt,V1,V2)) -> MARK(U25(isList(V1),V2)) ACTIVE(U25(tt,V2)) -> MARK(U26(isList(V2))) ACTIVE(U31(tt,V)) -> MARK(U32(isPalListKind(V),V)) ACTIVE(U32(tt,V)) -> MARK(U33(isQid(V))) ACTIVE(U41(tt,V1,V2)) -> MARK(U42(isPalListKind(V1),V1,V2)) ACTIVE(U42(tt,V1,V2)) -> MARK(U43(isPalListKind(V2),V1,V2)) ACTIVE(U43(tt,V1,V2)) -> MARK(U44(isPalListKind(V2),V1,V2)) ACTIVE(U44(tt,V1,V2)) -> MARK(U45(isList(V1),V2)) ACTIVE(U45(tt,V2)) -> MARK(U46(isNeList(V2))) ACTIVE(U51(tt,V1,V2)) -> MARK(U52(isPalListKind(V1),V1,V2)) ACTIVE(U52(tt,V1,V2)) -> MARK(U53(isPalListKind(V2),V1,V2)) ACTIVE(U53(tt,V1,V2)) -> MARK(U54(isPalListKind(V2),V1,V2)) ACTIVE(U54(tt,V1,V2)) -> MARK(U55(isNeList(V1),V2)) ACTIVE(U55(tt,V2)) -> MARK(U56(isList(V2))) ACTIVE(U61(tt,V)) -> MARK(U62(isPalListKind(V),V)) ACTIVE(U62(tt,V)) -> MARK(U63(isQid(V))) ACTIVE(U71(tt,I,P)) -> MARK(U72(isPalListKind(I),P)) ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U22(tt,V1,V2)) -> MARK(U23(isPalListKind(V2),V1,V2)) ACTIVE(U23(tt,V1,V2)) -> MARK(U24(isPalListKind(V2),V1,V2)) ACTIVE(U24(tt,V1,V2)) -> MARK(U25(isList(V1),V2)) ACTIVE(U25(tt,V2)) -> MARK(U26(isList(V2))) ACTIVE(U31(tt,V)) -> MARK(U32(isPalListKind(V),V)) ACTIVE(U32(tt,V)) -> MARK(U33(isQid(V))) ACTIVE(U41(tt,V1,V2)) -> MARK(U42(isPalListKind(V1),V1,V2)) ACTIVE(U42(tt,V1,V2)) -> MARK(U43(isPalListKind(V2),V1,V2)) ACTIVE(U43(tt,V1,V2)) -> MARK(U44(isPalListKind(V2),V1,V2)) ACTIVE(U44(tt,V1,V2)) -> MARK(U45(isList(V1),V2)) ACTIVE(U45(tt,V2)) -> MARK(U46(isNeList(V2))) ACTIVE(U51(tt,V1,V2)) -> MARK(U52(isPalListKind(V1),V1,V2)) ACTIVE(U52(tt,V1,V2)) -> MARK(U53(isPalListKind(V2),V1,V2)) ACTIVE(U53(tt,V1,V2)) -> MARK(U54(isPalListKind(V2),V1,V2)) ACTIVE(U54(tt,V1,V2)) -> MARK(U55(isNeList(V1),V2)) ACTIVE(U55(tt,V2)) -> MARK(U56(isList(V2))) ACTIVE(U61(tt,V)) -> MARK(U62(isPalListKind(V),V)) ACTIVE(U62(tt,V)) -> MARK(U63(isQid(V))) ACTIVE(U71(tt,I,P)) -> MARK(U72(isPalListKind(I),P)) ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U22(tt,V1,V2)) -> MARK(U23(isPalListKind(V2),V1,V2)) ACTIVE(U23(tt,V1,V2)) -> MARK(U24(isPalListKind(V2),V1,V2)) ACTIVE(U24(tt,V1,V2)) -> MARK(U25(isList(V1),V2)) ACTIVE(U25(tt,V2)) -> MARK(U26(isList(V2))) ACTIVE(U31(tt,V)) -> MARK(U32(isPalListKind(V),V)) ACTIVE(U32(tt,V)) -> MARK(U33(isQid(V))) ACTIVE(U41(tt,V1,V2)) -> MARK(U42(isPalListKind(V1),V1,V2)) ACTIVE(U42(tt,V1,V2)) -> MARK(U43(isPalListKind(V2),V1,V2)) ACTIVE(U43(tt,V1,V2)) -> MARK(U44(isPalListKind(V2),V1,V2)) ACTIVE(U44(tt,V1,V2)) -> MARK(U45(isList(V1),V2)) ACTIVE(U45(tt,V2)) -> MARK(U46(isNeList(V2))) ACTIVE(U51(tt,V1,V2)) -> MARK(U52(isPalListKind(V1),V1,V2)) ACTIVE(U52(tt,V1,V2)) -> MARK(U53(isPalListKind(V2),V1,V2)) ACTIVE(U53(tt,V1,V2)) -> MARK(U54(isPalListKind(V2),V1,V2)) ACTIVE(U54(tt,V1,V2)) -> MARK(U55(isNeList(V1),V2)) ACTIVE(U55(tt,V2)) -> MARK(U56(isList(V2))) ACTIVE(U61(tt,V)) -> MARK(U62(isPalListKind(V),V)) ACTIVE(U62(tt,V)) -> MARK(U63(isQid(V))) ACTIVE(U71(tt,I,P)) -> MARK(U72(isPalListKind(I),P)) ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = X1 + 2.X2 [U12](X1,X2) = X1 + 2.X2 [U13](X) = X [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U22](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U23](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U24](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U25](X1,X2) = X1 + 2.X2 + 1 [U26](X) = X [U31](X1,X2) = X1 + 2.X2 [U32](X1,X2) = X1 + 2.X2 [U33](X) = X [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U43](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U44](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U45](X1,X2) = X1 + 2.X2 + 2 [U46](X) = X + 2 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U52](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U53](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U54](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U55](X1,X2) = X1 + 2.X2 + 2 [U56](X) = X + 1 [U61](X1,X2) = X1 + 2.X2 [U62](X1,X2) = X1 [U63](X) = X [U71](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U72](X1,X2) = 2.X1 + 2.X2 + 2 [U73](X1,X2) = X1 + 2 [U74](X) = X + 2 [U81](X1,X2) = X1 + 2.X2 [U82](X1,X2) = X1 + 2.X2 [U83](X) = X [U91](X1,X2) = X1 [U92](X) = X [__](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 [isPalListKind](X) = 2 [isQid](X) = 2 [mark](X) = X [a] = 0 [e] = 0 [i] = 0 [nil] = 0 [o] = 0 [tt] = 2 [u] = 2 [ACTIVE](X) = 2.X + 2 [MARK](X) = 2.X + 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U23(tt,V1,V2)) -> MARK(U24(isPalListKind(V2),V1,V2)) ACTIVE(U24(tt,V1,V2)) -> MARK(U25(isList(V1),V2)) ACTIVE(U25(tt,V2)) -> MARK(U26(isList(V2))) ACTIVE(U31(tt,V)) -> MARK(U32(isPalListKind(V),V)) ACTIVE(U32(tt,V)) -> MARK(U33(isQid(V))) ACTIVE(U41(tt,V1,V2)) -> MARK(U42(isPalListKind(V1),V1,V2)) ACTIVE(U42(tt,V1,V2)) -> MARK(U43(isPalListKind(V2),V1,V2)) ACTIVE(U43(tt,V1,V2)) -> MARK(U44(isPalListKind(V2),V1,V2)) ACTIVE(U44(tt,V1,V2)) -> MARK(U45(isList(V1),V2)) ACTIVE(U45(tt,V2)) -> MARK(U46(isNeList(V2))) ACTIVE(U51(tt,V1,V2)) -> MARK(U52(isPalListKind(V1),V1,V2)) ACTIVE(U52(tt,V1,V2)) -> MARK(U53(isPalListKind(V2),V1,V2)) ACTIVE(U53(tt,V1,V2)) -> MARK(U54(isPalListKind(V2),V1,V2)) ACTIVE(U54(tt,V1,V2)) -> MARK(U55(isNeList(V1),V2)) ACTIVE(U55(tt,V2)) -> MARK(U56(isList(V2))) ACTIVE(U61(tt,V)) -> MARK(U62(isPalListKind(V),V)) ACTIVE(U62(tt,V)) -> MARK(U63(isQid(V))) ACTIVE(U71(tt,I,P)) -> MARK(U72(isPalListKind(I),P)) ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U23(tt,V1,V2)) -> MARK(U24(isPalListKind(V2),V1,V2)) ACTIVE(U24(tt,V1,V2)) -> MARK(U25(isList(V1),V2)) ACTIVE(U25(tt,V2)) -> MARK(U26(isList(V2))) ACTIVE(U31(tt,V)) -> MARK(U32(isPalListKind(V),V)) ACTIVE(U32(tt,V)) -> MARK(U33(isQid(V))) ACTIVE(U41(tt,V1,V2)) -> MARK(U42(isPalListKind(V1),V1,V2)) ACTIVE(U42(tt,V1,V2)) -> MARK(U43(isPalListKind(V2),V1,V2)) ACTIVE(U43(tt,V1,V2)) -> MARK(U44(isPalListKind(V2),V1,V2)) ACTIVE(U44(tt,V1,V2)) -> MARK(U45(isList(V1),V2)) ACTIVE(U45(tt,V2)) -> MARK(U46(isNeList(V2))) ACTIVE(U51(tt,V1,V2)) -> MARK(U52(isPalListKind(V1),V1,V2)) ACTIVE(U52(tt,V1,V2)) -> MARK(U53(isPalListKind(V2),V1,V2)) ACTIVE(U53(tt,V1,V2)) -> MARK(U54(isPalListKind(V2),V1,V2)) ACTIVE(U54(tt,V1,V2)) -> MARK(U55(isNeList(V1),V2)) ACTIVE(U55(tt,V2)) -> MARK(U56(isList(V2))) ACTIVE(U61(tt,V)) -> MARK(U62(isPalListKind(V),V)) ACTIVE(U62(tt,V)) -> MARK(U63(isQid(V))) ACTIVE(U71(tt,I,P)) -> MARK(U72(isPalListKind(I),P)) ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U23(tt,V1,V2)) -> MARK(U24(isPalListKind(V2),V1,V2)) ACTIVE(U24(tt,V1,V2)) -> MARK(U25(isList(V1),V2)) ACTIVE(U25(tt,V2)) -> MARK(U26(isList(V2))) ACTIVE(U31(tt,V)) -> MARK(U32(isPalListKind(V),V)) ACTIVE(U32(tt,V)) -> MARK(U33(isQid(V))) ACTIVE(U41(tt,V1,V2)) -> MARK(U42(isPalListKind(V1),V1,V2)) ACTIVE(U42(tt,V1,V2)) -> MARK(U43(isPalListKind(V2),V1,V2)) ACTIVE(U43(tt,V1,V2)) -> MARK(U44(isPalListKind(V2),V1,V2)) ACTIVE(U44(tt,V1,V2)) -> MARK(U45(isList(V1),V2)) ACTIVE(U45(tt,V2)) -> MARK(U46(isNeList(V2))) ACTIVE(U51(tt,V1,V2)) -> MARK(U52(isPalListKind(V1),V1,V2)) ACTIVE(U52(tt,V1,V2)) -> MARK(U53(isPalListKind(V2),V1,V2)) ACTIVE(U53(tt,V1,V2)) -> MARK(U54(isPalListKind(V2),V1,V2)) ACTIVE(U54(tt,V1,V2)) -> MARK(U55(isNeList(V1),V2)) ACTIVE(U55(tt,V2)) -> MARK(U56(isList(V2))) ACTIVE(U61(tt,V)) -> MARK(U62(isPalListKind(V),V)) ACTIVE(U62(tt,V)) -> MARK(U63(isQid(V))) ACTIVE(U71(tt,I,P)) -> MARK(U72(isPalListKind(I),P)) ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = X1 + 2.X2 [U12](X1,X2) = X1 + 2.X2 [U13](X) = X [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U22](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U23](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U24](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 1 [U25](X1,X2) = X1 + 2.X2 + 2 [U26](X) = X + 2 [U31](X1,X2) = X1 + 2.X2 [U32](X1,X2) = X1 + 2.X2 [U33](X) = X + 2 [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U43](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U44](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U45](X1,X2) = X1 + 2.X2 + 2 [U46](X) = X + 2 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U52](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U53](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U54](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U55](X1,X2) = X1 + 2.X2 + 2 [U56](X) = X [U61](X1,X2) = X1 + 2.X2 [U62](X1,X2) = X1 + 2.X2 [U63](X) = 2.X + 1 [U71](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U72](X1,X2) = X1 + 2.X2 + 2 [U73](X1,X2) = X1 + 2 [U74](X) = X + 1 [U81](X1,X2) = X1 + 2.X2 [U82](X1,X2) = X1 + 2.X2 [U83](X) = X [U91](X1,X2) = X1 [U92](X) = X [__](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 [isPalListKind](X) = 2 [isQid](X) = X [mark](X) = X [a] = 2 [e] = 2 [i] = 2 [nil] = 2 [o] = 2 [tt] = 2 [u] = 2 [ACTIVE](X) = 2.X + 2 [MARK](X) = 2.X + 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U24(tt,V1,V2)) -> MARK(U25(isList(V1),V2)) ACTIVE(U25(tt,V2)) -> MARK(U26(isList(V2))) ACTIVE(U31(tt,V)) -> MARK(U32(isPalListKind(V),V)) ACTIVE(U32(tt,V)) -> MARK(U33(isQid(V))) ACTIVE(U41(tt,V1,V2)) -> MARK(U42(isPalListKind(V1),V1,V2)) ACTIVE(U42(tt,V1,V2)) -> MARK(U43(isPalListKind(V2),V1,V2)) ACTIVE(U43(tt,V1,V2)) -> MARK(U44(isPalListKind(V2),V1,V2)) ACTIVE(U44(tt,V1,V2)) -> MARK(U45(isList(V1),V2)) ACTIVE(U45(tt,V2)) -> MARK(U46(isNeList(V2))) ACTIVE(U51(tt,V1,V2)) -> MARK(U52(isPalListKind(V1),V1,V2)) ACTIVE(U52(tt,V1,V2)) -> MARK(U53(isPalListKind(V2),V1,V2)) ACTIVE(U53(tt,V1,V2)) -> MARK(U54(isPalListKind(V2),V1,V2)) ACTIVE(U54(tt,V1,V2)) -> MARK(U55(isNeList(V1),V2)) ACTIVE(U55(tt,V2)) -> MARK(U56(isList(V2))) ACTIVE(U61(tt,V)) -> MARK(U62(isPalListKind(V),V)) ACTIVE(U62(tt,V)) -> MARK(U63(isQid(V))) ACTIVE(U71(tt,I,P)) -> MARK(U72(isPalListKind(I),P)) ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U24(tt,V1,V2)) -> MARK(U25(isList(V1),V2)) ACTIVE(U25(tt,V2)) -> MARK(U26(isList(V2))) ACTIVE(U31(tt,V)) -> MARK(U32(isPalListKind(V),V)) ACTIVE(U32(tt,V)) -> MARK(U33(isQid(V))) ACTIVE(U41(tt,V1,V2)) -> MARK(U42(isPalListKind(V1),V1,V2)) ACTIVE(U42(tt,V1,V2)) -> MARK(U43(isPalListKind(V2),V1,V2)) ACTIVE(U43(tt,V1,V2)) -> MARK(U44(isPalListKind(V2),V1,V2)) ACTIVE(U44(tt,V1,V2)) -> MARK(U45(isList(V1),V2)) ACTIVE(U45(tt,V2)) -> MARK(U46(isNeList(V2))) ACTIVE(U51(tt,V1,V2)) -> MARK(U52(isPalListKind(V1),V1,V2)) ACTIVE(U52(tt,V1,V2)) -> MARK(U53(isPalListKind(V2),V1,V2)) ACTIVE(U53(tt,V1,V2)) -> MARK(U54(isPalListKind(V2),V1,V2)) ACTIVE(U54(tt,V1,V2)) -> MARK(U55(isNeList(V1),V2)) ACTIVE(U55(tt,V2)) -> MARK(U56(isList(V2))) ACTIVE(U61(tt,V)) -> MARK(U62(isPalListKind(V),V)) ACTIVE(U62(tt,V)) -> MARK(U63(isQid(V))) ACTIVE(U71(tt,I,P)) -> MARK(U72(isPalListKind(I),P)) ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U24(tt,V1,V2)) -> MARK(U25(isList(V1),V2)) ACTIVE(U25(tt,V2)) -> MARK(U26(isList(V2))) ACTIVE(U31(tt,V)) -> MARK(U32(isPalListKind(V),V)) ACTIVE(U32(tt,V)) -> MARK(U33(isQid(V))) ACTIVE(U41(tt,V1,V2)) -> MARK(U42(isPalListKind(V1),V1,V2)) ACTIVE(U42(tt,V1,V2)) -> MARK(U43(isPalListKind(V2),V1,V2)) ACTIVE(U43(tt,V1,V2)) -> MARK(U44(isPalListKind(V2),V1,V2)) ACTIVE(U44(tt,V1,V2)) -> MARK(U45(isList(V1),V2)) ACTIVE(U45(tt,V2)) -> MARK(U46(isNeList(V2))) ACTIVE(U51(tt,V1,V2)) -> MARK(U52(isPalListKind(V1),V1,V2)) ACTIVE(U52(tt,V1,V2)) -> MARK(U53(isPalListKind(V2),V1,V2)) ACTIVE(U53(tt,V1,V2)) -> MARK(U54(isPalListKind(V2),V1,V2)) ACTIVE(U54(tt,V1,V2)) -> MARK(U55(isNeList(V1),V2)) ACTIVE(U55(tt,V2)) -> MARK(U56(isList(V2))) ACTIVE(U61(tt,V)) -> MARK(U62(isPalListKind(V),V)) ACTIVE(U62(tt,V)) -> MARK(U63(isQid(V))) ACTIVE(U71(tt,I,P)) -> MARK(U72(isPalListKind(I),P)) ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = X1 + 2.X2 [U12](X1,X2) = X1 + 2.X2 [U13](X) = X [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U22](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U23](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U24](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 [U25](X1,X2) = X1 + 2.X2 + 1 [U26](X) = X + 1 [U31](X1,X2) = X1 + 2.X2 [U32](X1,X2) = X1 + 2.X2 [U33](X) = X [U41](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 [U43](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U44](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 [U45](X1,X2) = X1 + 2.X2 + 2 [U46](X) = X [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 [U52](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U53](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U54](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U55](X1,X2) = X1 + 2.X2 + 2 [U56](X) = X + 2 [U61](X1,X2) = X1 + 2.X2 [U62](X1,X2) = X1 + 2.X2 [U63](X) = X [U71](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U72](X1,X2) = 2.X1 + 2.X2 [U73](X1,X2) = X1 + 2 [U74](X) = 2.X [U81](X1,X2) = X1 + 2.X2 [U82](X1,X2) = X1 + 2.X2 [U83](X) = X [U91](X1,X2) = X1 [U92](X) = X [__](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 [isPalListKind](X) = 2 [isQid](X) = 2 [mark](X) = X [a] = 0 [e] = 2 [i] = 2 [nil] = 2 [o] = 2 [tt] = 2 [u] = 2 [ACTIVE](X) = 2.X + 2 [MARK](X) = 2.X + 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U25(tt,V2)) -> MARK(U26(isList(V2))) ACTIVE(U31(tt,V)) -> MARK(U32(isPalListKind(V),V)) ACTIVE(U32(tt,V)) -> MARK(U33(isQid(V))) ACTIVE(U41(tt,V1,V2)) -> MARK(U42(isPalListKind(V1),V1,V2)) ACTIVE(U42(tt,V1,V2)) -> MARK(U43(isPalListKind(V2),V1,V2)) ACTIVE(U43(tt,V1,V2)) -> MARK(U44(isPalListKind(V2),V1,V2)) ACTIVE(U44(tt,V1,V2)) -> MARK(U45(isList(V1),V2)) ACTIVE(U45(tt,V2)) -> MARK(U46(isNeList(V2))) ACTIVE(U51(tt,V1,V2)) -> MARK(U52(isPalListKind(V1),V1,V2)) ACTIVE(U52(tt,V1,V2)) -> MARK(U53(isPalListKind(V2),V1,V2)) ACTIVE(U53(tt,V1,V2)) -> MARK(U54(isPalListKind(V2),V1,V2)) ACTIVE(U54(tt,V1,V2)) -> MARK(U55(isNeList(V1),V2)) ACTIVE(U55(tt,V2)) -> MARK(U56(isList(V2))) ACTIVE(U61(tt,V)) -> MARK(U62(isPalListKind(V),V)) ACTIVE(U62(tt,V)) -> MARK(U63(isQid(V))) ACTIVE(U71(tt,I,P)) -> MARK(U72(isPalListKind(I),P)) ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U25(tt,V2)) -> MARK(U26(isList(V2))) ACTIVE(U31(tt,V)) -> MARK(U32(isPalListKind(V),V)) ACTIVE(U32(tt,V)) -> MARK(U33(isQid(V))) ACTIVE(U41(tt,V1,V2)) -> MARK(U42(isPalListKind(V1),V1,V2)) ACTIVE(U42(tt,V1,V2)) -> MARK(U43(isPalListKind(V2),V1,V2)) ACTIVE(U43(tt,V1,V2)) -> MARK(U44(isPalListKind(V2),V1,V2)) ACTIVE(U44(tt,V1,V2)) -> MARK(U45(isList(V1),V2)) ACTIVE(U45(tt,V2)) -> MARK(U46(isNeList(V2))) ACTIVE(U51(tt,V1,V2)) -> MARK(U52(isPalListKind(V1),V1,V2)) ACTIVE(U52(tt,V1,V2)) -> MARK(U53(isPalListKind(V2),V1,V2)) ACTIVE(U53(tt,V1,V2)) -> MARK(U54(isPalListKind(V2),V1,V2)) ACTIVE(U54(tt,V1,V2)) -> MARK(U55(isNeList(V1),V2)) ACTIVE(U55(tt,V2)) -> MARK(U56(isList(V2))) ACTIVE(U61(tt,V)) -> MARK(U62(isPalListKind(V),V)) ACTIVE(U62(tt,V)) -> MARK(U63(isQid(V))) ACTIVE(U71(tt,I,P)) -> MARK(U72(isPalListKind(I),P)) ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U25(tt,V2)) -> MARK(U26(isList(V2))) ACTIVE(U31(tt,V)) -> MARK(U32(isPalListKind(V),V)) ACTIVE(U32(tt,V)) -> MARK(U33(isQid(V))) ACTIVE(U41(tt,V1,V2)) -> MARK(U42(isPalListKind(V1),V1,V2)) ACTIVE(U42(tt,V1,V2)) -> MARK(U43(isPalListKind(V2),V1,V2)) ACTIVE(U43(tt,V1,V2)) -> MARK(U44(isPalListKind(V2),V1,V2)) ACTIVE(U44(tt,V1,V2)) -> MARK(U45(isList(V1),V2)) ACTIVE(U45(tt,V2)) -> MARK(U46(isNeList(V2))) ACTIVE(U51(tt,V1,V2)) -> MARK(U52(isPalListKind(V1),V1,V2)) ACTIVE(U52(tt,V1,V2)) -> MARK(U53(isPalListKind(V2),V1,V2)) ACTIVE(U53(tt,V1,V2)) -> MARK(U54(isPalListKind(V2),V1,V2)) ACTIVE(U54(tt,V1,V2)) -> MARK(U55(isNeList(V1),V2)) ACTIVE(U55(tt,V2)) -> MARK(U56(isList(V2))) ACTIVE(U61(tt,V)) -> MARK(U62(isPalListKind(V),V)) ACTIVE(U62(tt,V)) -> MARK(U63(isQid(V))) ACTIVE(U71(tt,I,P)) -> MARK(U72(isPalListKind(I),P)) ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = X1 + 2.X2 [U12](X1,X2) = X1 + 2.X2 [U13](X) = X [U21](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U22](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U23](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U24](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U25](X1,X2) = X1 + 2.X2 + 2 [U26](X) = X + 1 [U31](X1,X2) = X1 + 2.X2 [U32](X1,X2) = X1 + 2.X2 [U33](X) = X [U41](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U43](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 [U44](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U45](X1,X2) = X1 + 2.X2 [U46](X) = X [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U52](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U53](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U54](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U55](X1,X2) = X1 + 2.X2 + 2 [U56](X) = X + 2 [U61](X1,X2) = X1 + 2.X2 [U62](X1,X2) = X1 + 2.X2 [U63](X) = X [U71](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U72](X1,X2) = 2.X1 + 2.X2 + 2 [U73](X1,X2) = X1 + 2 [U74](X) = 2.X [U81](X1,X2) = X1 + 2.X2 [U82](X1,X2) = X1 + 2.X2 [U83](X) = X [U91](X1,X2) = X1 [U92](X) = X [__](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 [isPalListKind](X) = 2 [isQid](X) = 2 [mark](X) = X [a] = 2 [e] = 2 [i] = 2 [nil] = 0 [o] = 0 [tt] = 2 [u] = 2 [ACTIVE](X) = 2.X + 1 [MARK](X) = 2.X + 1 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U31(tt,V)) -> MARK(U32(isPalListKind(V),V)) ACTIVE(U32(tt,V)) -> MARK(U33(isQid(V))) ACTIVE(U41(tt,V1,V2)) -> MARK(U42(isPalListKind(V1),V1,V2)) ACTIVE(U42(tt,V1,V2)) -> MARK(U43(isPalListKind(V2),V1,V2)) ACTIVE(U43(tt,V1,V2)) -> MARK(U44(isPalListKind(V2),V1,V2)) ACTIVE(U44(tt,V1,V2)) -> MARK(U45(isList(V1),V2)) ACTIVE(U45(tt,V2)) -> MARK(U46(isNeList(V2))) ACTIVE(U51(tt,V1,V2)) -> MARK(U52(isPalListKind(V1),V1,V2)) ACTIVE(U52(tt,V1,V2)) -> MARK(U53(isPalListKind(V2),V1,V2)) ACTIVE(U53(tt,V1,V2)) -> MARK(U54(isPalListKind(V2),V1,V2)) ACTIVE(U54(tt,V1,V2)) -> MARK(U55(isNeList(V1),V2)) ACTIVE(U55(tt,V2)) -> MARK(U56(isList(V2))) ACTIVE(U61(tt,V)) -> MARK(U62(isPalListKind(V),V)) ACTIVE(U62(tt,V)) -> MARK(U63(isQid(V))) ACTIVE(U71(tt,I,P)) -> MARK(U72(isPalListKind(I),P)) ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U31(tt,V)) -> MARK(U32(isPalListKind(V),V)) ACTIVE(U32(tt,V)) -> MARK(U33(isQid(V))) ACTIVE(U41(tt,V1,V2)) -> MARK(U42(isPalListKind(V1),V1,V2)) ACTIVE(U42(tt,V1,V2)) -> MARK(U43(isPalListKind(V2),V1,V2)) ACTIVE(U43(tt,V1,V2)) -> MARK(U44(isPalListKind(V2),V1,V2)) ACTIVE(U44(tt,V1,V2)) -> MARK(U45(isList(V1),V2)) ACTIVE(U45(tt,V2)) -> MARK(U46(isNeList(V2))) ACTIVE(U51(tt,V1,V2)) -> MARK(U52(isPalListKind(V1),V1,V2)) ACTIVE(U52(tt,V1,V2)) -> MARK(U53(isPalListKind(V2),V1,V2)) ACTIVE(U53(tt,V1,V2)) -> MARK(U54(isPalListKind(V2),V1,V2)) ACTIVE(U54(tt,V1,V2)) -> MARK(U55(isNeList(V1),V2)) ACTIVE(U55(tt,V2)) -> MARK(U56(isList(V2))) ACTIVE(U61(tt,V)) -> MARK(U62(isPalListKind(V),V)) ACTIVE(U62(tt,V)) -> MARK(U63(isQid(V))) ACTIVE(U71(tt,I,P)) -> MARK(U72(isPalListKind(I),P)) ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U31(tt,V)) -> MARK(U32(isPalListKind(V),V)) ACTIVE(U32(tt,V)) -> MARK(U33(isQid(V))) ACTIVE(U41(tt,V1,V2)) -> MARK(U42(isPalListKind(V1),V1,V2)) ACTIVE(U42(tt,V1,V2)) -> MARK(U43(isPalListKind(V2),V1,V2)) ACTIVE(U43(tt,V1,V2)) -> MARK(U44(isPalListKind(V2),V1,V2)) ACTIVE(U44(tt,V1,V2)) -> MARK(U45(isList(V1),V2)) ACTIVE(U45(tt,V2)) -> MARK(U46(isNeList(V2))) ACTIVE(U51(tt,V1,V2)) -> MARK(U52(isPalListKind(V1),V1,V2)) ACTIVE(U52(tt,V1,V2)) -> MARK(U53(isPalListKind(V2),V1,V2)) ACTIVE(U53(tt,V1,V2)) -> MARK(U54(isPalListKind(V2),V1,V2)) ACTIVE(U54(tt,V1,V2)) -> MARK(U55(isNeList(V1),V2)) ACTIVE(U55(tt,V2)) -> MARK(U56(isList(V2))) ACTIVE(U61(tt,V)) -> MARK(U62(isPalListKind(V),V)) ACTIVE(U62(tt,V)) -> MARK(U63(isQid(V))) ACTIVE(U71(tt,I,P)) -> MARK(U72(isPalListKind(I),P)) ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = 2.X1 + 2.X2 + 1 [U12](X1,X2) = 2.X1 + 2.X2 + 1 [U13](X) = X [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U22](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U23](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U24](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U25](X1,X2) = X1 + 2.X2 + 1 [U26](X) = X [U31](X1,X2) = 2.X1 + 2.X2 + 1 [U32](X1,X2) = 2.X1 + 2.X2 [U33](X) = 2.X [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U43](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U44](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U45](X1,X2) = X1 + 2.X2 + 1 [U46](X) = X [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U52](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U53](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U54](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U55](X1,X2) = X1 + 2.X2 + 1 [U56](X) = X [U61](X1,X2) = 2.X1 + X2 + 2 [U62](X1,X2) = 2.X1 + X2 + 2 [U63](X) = 2.X + 2 [U71](X1,X2,X3) = X1 + X2 + 2.X3 + 2 [U72](X1,X2) = 2.X1 + X2 + 2 [U73](X1,X2) = X1 [U74](X) = 2.X [U81](X1,X2) = 2.X1 + X2 + 2 [U82](X1,X2) = 2.X1 + X2 + 2 [U83](X) = X [U91](X1,X2) = 2.X1 [U92](X) = 2.X [__](X1,X2) = 2.X1 + X2 + 2 [active](X) = X [isList](X) = 2.X + 1 [isNeList](X) = 2.X + 1 [isNePal](X) = X + 2 [isPal](X) = X + 2 [isPalListKind](X) = 0 [isQid](X) = 0 [mark](X) = X [a] = 0 [e] = 1 [i] = 2 [nil] = 1 [o] = 2 [tt] = 0 [u] = 0 [ACTIVE](X) = 2.X + 2 [MARK](X) = 2.X + 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U32(tt,V)) -> MARK(U33(isQid(V))) ACTIVE(U41(tt,V1,V2)) -> MARK(U42(isPalListKind(V1),V1,V2)) ACTIVE(U42(tt,V1,V2)) -> MARK(U43(isPalListKind(V2),V1,V2)) ACTIVE(U43(tt,V1,V2)) -> MARK(U44(isPalListKind(V2),V1,V2)) ACTIVE(U44(tt,V1,V2)) -> MARK(U45(isList(V1),V2)) ACTIVE(U45(tt,V2)) -> MARK(U46(isNeList(V2))) ACTIVE(U51(tt,V1,V2)) -> MARK(U52(isPalListKind(V1),V1,V2)) ACTIVE(U52(tt,V1,V2)) -> MARK(U53(isPalListKind(V2),V1,V2)) ACTIVE(U53(tt,V1,V2)) -> MARK(U54(isPalListKind(V2),V1,V2)) ACTIVE(U54(tt,V1,V2)) -> MARK(U55(isNeList(V1),V2)) ACTIVE(U55(tt,V2)) -> MARK(U56(isList(V2))) ACTIVE(U61(tt,V)) -> MARK(U62(isPalListKind(V),V)) ACTIVE(U62(tt,V)) -> MARK(U63(isQid(V))) ACTIVE(U71(tt,I,P)) -> MARK(U72(isPalListKind(I),P)) ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U32(tt,V)) -> MARK(U33(isQid(V))) ACTIVE(U41(tt,V1,V2)) -> MARK(U42(isPalListKind(V1),V1,V2)) ACTIVE(U42(tt,V1,V2)) -> MARK(U43(isPalListKind(V2),V1,V2)) ACTIVE(U43(tt,V1,V2)) -> MARK(U44(isPalListKind(V2),V1,V2)) ACTIVE(U44(tt,V1,V2)) -> MARK(U45(isList(V1),V2)) ACTIVE(U45(tt,V2)) -> MARK(U46(isNeList(V2))) ACTIVE(U51(tt,V1,V2)) -> MARK(U52(isPalListKind(V1),V1,V2)) ACTIVE(U52(tt,V1,V2)) -> MARK(U53(isPalListKind(V2),V1,V2)) ACTIVE(U53(tt,V1,V2)) -> MARK(U54(isPalListKind(V2),V1,V2)) ACTIVE(U54(tt,V1,V2)) -> MARK(U55(isNeList(V1),V2)) ACTIVE(U55(tt,V2)) -> MARK(U56(isList(V2))) ACTIVE(U61(tt,V)) -> MARK(U62(isPalListKind(V),V)) ACTIVE(U62(tt,V)) -> MARK(U63(isQid(V))) ACTIVE(U71(tt,I,P)) -> MARK(U72(isPalListKind(I),P)) ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U32(tt,V)) -> MARK(U33(isQid(V))) ACTIVE(U41(tt,V1,V2)) -> MARK(U42(isPalListKind(V1),V1,V2)) ACTIVE(U42(tt,V1,V2)) -> MARK(U43(isPalListKind(V2),V1,V2)) ACTIVE(U43(tt,V1,V2)) -> MARK(U44(isPalListKind(V2),V1,V2)) ACTIVE(U44(tt,V1,V2)) -> MARK(U45(isList(V1),V2)) ACTIVE(U45(tt,V2)) -> MARK(U46(isNeList(V2))) ACTIVE(U51(tt,V1,V2)) -> MARK(U52(isPalListKind(V1),V1,V2)) ACTIVE(U52(tt,V1,V2)) -> MARK(U53(isPalListKind(V2),V1,V2)) ACTIVE(U53(tt,V1,V2)) -> MARK(U54(isPalListKind(V2),V1,V2)) ACTIVE(U54(tt,V1,V2)) -> MARK(U55(isNeList(V1),V2)) ACTIVE(U55(tt,V2)) -> MARK(U56(isList(V2))) ACTIVE(U61(tt,V)) -> MARK(U62(isPalListKind(V),V)) ACTIVE(U62(tt,V)) -> MARK(U63(isQid(V))) ACTIVE(U71(tt,I,P)) -> MARK(U72(isPalListKind(I),P)) ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = X1 + 2.X2 [U12](X1,X2) = X1 + 2.X2 [U13](X) = X [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 1 [U22](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 1 [U23](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U24](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 [U25](X1,X2) = X1 + 2.X2 + 2 [U26](X) = X + 2 [U31](X1,X2) = X1 + 2.X2 [U32](X1,X2) = X1 + X2 [U33](X) = X [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U43](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U44](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U45](X1,X2) = X1 + 2.X2 + 2 [U46](X) = X + 2 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U52](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U53](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U54](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U55](X1,X2) = X1 + 2.X2 [U56](X) = X [U61](X1,X2) = X1 + 2.X2 [U62](X1,X2) = X1 + 2.X2 [U63](X) = 2.X [U71](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U72](X1,X2) = 2.X1 + 2.X2 + 2 [U73](X1,X2) = X1 + 2 [U74](X) = 2.X [U81](X1,X2) = X1 + 2.X2 [U82](X1,X2) = X1 + 2.X2 [U83](X) = X [U91](X1,X2) = X1 [U92](X) = X [__](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 [isPalListKind](X) = 2 [isQid](X) = X + 1 [mark](X) = X [a] = 2 [e] = 2 [i] = 2 [nil] = 2 [o] = 2 [tt] = 2 [u] = 2 [ACTIVE](X) = 2.X + 2 [MARK](X) = 2.X + 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U41(tt,V1,V2)) -> MARK(U42(isPalListKind(V1),V1,V2)) ACTIVE(U42(tt,V1,V2)) -> MARK(U43(isPalListKind(V2),V1,V2)) ACTIVE(U43(tt,V1,V2)) -> MARK(U44(isPalListKind(V2),V1,V2)) ACTIVE(U44(tt,V1,V2)) -> MARK(U45(isList(V1),V2)) ACTIVE(U45(tt,V2)) -> MARK(U46(isNeList(V2))) ACTIVE(U51(tt,V1,V2)) -> MARK(U52(isPalListKind(V1),V1,V2)) ACTIVE(U52(tt,V1,V2)) -> MARK(U53(isPalListKind(V2),V1,V2)) ACTIVE(U53(tt,V1,V2)) -> MARK(U54(isPalListKind(V2),V1,V2)) ACTIVE(U54(tt,V1,V2)) -> MARK(U55(isNeList(V1),V2)) ACTIVE(U55(tt,V2)) -> MARK(U56(isList(V2))) ACTIVE(U61(tt,V)) -> MARK(U62(isPalListKind(V),V)) ACTIVE(U62(tt,V)) -> MARK(U63(isQid(V))) ACTIVE(U71(tt,I,P)) -> MARK(U72(isPalListKind(I),P)) ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U41(tt,V1,V2)) -> MARK(U42(isPalListKind(V1),V1,V2)) ACTIVE(U42(tt,V1,V2)) -> MARK(U43(isPalListKind(V2),V1,V2)) ACTIVE(U43(tt,V1,V2)) -> MARK(U44(isPalListKind(V2),V1,V2)) ACTIVE(U44(tt,V1,V2)) -> MARK(U45(isList(V1),V2)) ACTIVE(U45(tt,V2)) -> MARK(U46(isNeList(V2))) ACTIVE(U51(tt,V1,V2)) -> MARK(U52(isPalListKind(V1),V1,V2)) ACTIVE(U52(tt,V1,V2)) -> MARK(U53(isPalListKind(V2),V1,V2)) ACTIVE(U53(tt,V1,V2)) -> MARK(U54(isPalListKind(V2),V1,V2)) ACTIVE(U54(tt,V1,V2)) -> MARK(U55(isNeList(V1),V2)) ACTIVE(U55(tt,V2)) -> MARK(U56(isList(V2))) ACTIVE(U61(tt,V)) -> MARK(U62(isPalListKind(V),V)) ACTIVE(U62(tt,V)) -> MARK(U63(isQid(V))) ACTIVE(U71(tt,I,P)) -> MARK(U72(isPalListKind(I),P)) ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U41(tt,V1,V2)) -> MARK(U42(isPalListKind(V1),V1,V2)) ACTIVE(U42(tt,V1,V2)) -> MARK(U43(isPalListKind(V2),V1,V2)) ACTIVE(U43(tt,V1,V2)) -> MARK(U44(isPalListKind(V2),V1,V2)) ACTIVE(U44(tt,V1,V2)) -> MARK(U45(isList(V1),V2)) ACTIVE(U45(tt,V2)) -> MARK(U46(isNeList(V2))) ACTIVE(U51(tt,V1,V2)) -> MARK(U52(isPalListKind(V1),V1,V2)) ACTIVE(U52(tt,V1,V2)) -> MARK(U53(isPalListKind(V2),V1,V2)) ACTIVE(U53(tt,V1,V2)) -> MARK(U54(isPalListKind(V2),V1,V2)) ACTIVE(U54(tt,V1,V2)) -> MARK(U55(isNeList(V1),V2)) ACTIVE(U55(tt,V2)) -> MARK(U56(isList(V2))) ACTIVE(U61(tt,V)) -> MARK(U62(isPalListKind(V),V)) ACTIVE(U62(tt,V)) -> MARK(U63(isQid(V))) ACTIVE(U71(tt,I,P)) -> MARK(U72(isPalListKind(I),P)) ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = X1 + 2.X2 [U12](X1,X2) = X1 + 2.X2 [U13](X) = X [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U22](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U23](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U24](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U25](X1,X2) = X1 + 2.X2 + 2 [U26](X) = X + 2 [U31](X1,X2) = X1 + X2 [U32](X1,X2) = X1 + X2 [U33](X) = X [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U43](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 [U44](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U45](X1,X2) = X1 + 2.X2 + 2 [U46](X) = X + 1 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U52](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U53](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U54](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U55](X1,X2) = X1 + 2.X2 + 2 [U56](X) = X + 2 [U61](X1,X2) = X1 + 2.X2 [U62](X1,X2) = X1 + 2.X2 [U63](X) = X [U71](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U72](X1,X2) = X1 + 2.X2 + 2 [U73](X1,X2) = X1 + 2 [U74](X) = X + 1 [U81](X1,X2) = X1 + 2.X2 [U82](X1,X2) = X1 + 2.X2 [U83](X) = X [U91](X1,X2) = X1 [U92](X) = X [__](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 [isPalListKind](X) = 2 [isQid](X) = 2 [mark](X) = X [a] = 0 [e] = 1 [i] = 2 [nil] = 2 [o] = 2 [tt] = 2 [u] = 2 [ACTIVE](X) = 2.X [MARK](X) = 2.X Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U42(tt,V1,V2)) -> MARK(U43(isPalListKind(V2),V1,V2)) ACTIVE(U43(tt,V1,V2)) -> MARK(U44(isPalListKind(V2),V1,V2)) ACTIVE(U44(tt,V1,V2)) -> MARK(U45(isList(V1),V2)) ACTIVE(U45(tt,V2)) -> MARK(U46(isNeList(V2))) ACTIVE(U51(tt,V1,V2)) -> MARK(U52(isPalListKind(V1),V1,V2)) ACTIVE(U52(tt,V1,V2)) -> MARK(U53(isPalListKind(V2),V1,V2)) ACTIVE(U53(tt,V1,V2)) -> MARK(U54(isPalListKind(V2),V1,V2)) ACTIVE(U54(tt,V1,V2)) -> MARK(U55(isNeList(V1),V2)) ACTIVE(U55(tt,V2)) -> MARK(U56(isList(V2))) ACTIVE(U61(tt,V)) -> MARK(U62(isPalListKind(V),V)) ACTIVE(U62(tt,V)) -> MARK(U63(isQid(V))) ACTIVE(U71(tt,I,P)) -> MARK(U72(isPalListKind(I),P)) ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U42(tt,V1,V2)) -> MARK(U43(isPalListKind(V2),V1,V2)) ACTIVE(U43(tt,V1,V2)) -> MARK(U44(isPalListKind(V2),V1,V2)) ACTIVE(U44(tt,V1,V2)) -> MARK(U45(isList(V1),V2)) ACTIVE(U45(tt,V2)) -> MARK(U46(isNeList(V2))) ACTIVE(U51(tt,V1,V2)) -> MARK(U52(isPalListKind(V1),V1,V2)) ACTIVE(U52(tt,V1,V2)) -> MARK(U53(isPalListKind(V2),V1,V2)) ACTIVE(U53(tt,V1,V2)) -> MARK(U54(isPalListKind(V2),V1,V2)) ACTIVE(U54(tt,V1,V2)) -> MARK(U55(isNeList(V1),V2)) ACTIVE(U55(tt,V2)) -> MARK(U56(isList(V2))) ACTIVE(U61(tt,V)) -> MARK(U62(isPalListKind(V),V)) ACTIVE(U62(tt,V)) -> MARK(U63(isQid(V))) ACTIVE(U71(tt,I,P)) -> MARK(U72(isPalListKind(I),P)) ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U42(tt,V1,V2)) -> MARK(U43(isPalListKind(V2),V1,V2)) ACTIVE(U43(tt,V1,V2)) -> MARK(U44(isPalListKind(V2),V1,V2)) ACTIVE(U44(tt,V1,V2)) -> MARK(U45(isList(V1),V2)) ACTIVE(U45(tt,V2)) -> MARK(U46(isNeList(V2))) ACTIVE(U51(tt,V1,V2)) -> MARK(U52(isPalListKind(V1),V1,V2)) ACTIVE(U52(tt,V1,V2)) -> MARK(U53(isPalListKind(V2),V1,V2)) ACTIVE(U53(tt,V1,V2)) -> MARK(U54(isPalListKind(V2),V1,V2)) ACTIVE(U54(tt,V1,V2)) -> MARK(U55(isNeList(V1),V2)) ACTIVE(U55(tt,V2)) -> MARK(U56(isList(V2))) ACTIVE(U61(tt,V)) -> MARK(U62(isPalListKind(V),V)) ACTIVE(U62(tt,V)) -> MARK(U63(isQid(V))) ACTIVE(U71(tt,I,P)) -> MARK(U72(isPalListKind(I),P)) ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = X1 + 2.X2 [U12](X1,X2) = X1 + 2.X2 [U13](X) = X [U21](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U22](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U23](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U24](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U25](X1,X2) = X1 + 2.X2 + 1 [U26](X) = X + 1 [U31](X1,X2) = X1 + X2 [U32](X1,X2) = X1 + X2 [U33](X) = X [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U43](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U44](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U45](X1,X2) = X1 + 2.X2 + 2 [U46](X) = X + 2 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U52](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U53](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 [U54](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U55](X1,X2) = X1 + 2.X2 + 2 [U56](X) = X + 2 [U61](X1,X2) = X1 [U62](X1,X2) = X1 [U63](X) = X [U71](X1,X2,X3) = X1 [U72](X1,X2) = X1 [U73](X1,X2) = X1 [U74](X) = X [U81](X1,X2) = X1 [U82](X1,X2) = X1 [U83](X) = X [U91](X1,X2) = X1 [U92](X) = X [__](X1,X2) = 2.X1 + X2 + 2 [active](X) = X [isList](X) = 2.X + 2 [isNeList](X) = 2.X + 2 [isNePal](X) = 2 [isPal](X) = 2 [isPalListKind](X) = 2 [isQid](X) = 2 [mark](X) = X [a] = 0 [e] = 0 [i] = 1 [nil] = 2 [o] = 2 [tt] = 2 [u] = 0 [ACTIVE](X) = 2.X + 2 [MARK](X) = 2.X + 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U43(tt,V1,V2)) -> MARK(U44(isPalListKind(V2),V1,V2)) ACTIVE(U44(tt,V1,V2)) -> MARK(U45(isList(V1),V2)) ACTIVE(U45(tt,V2)) -> MARK(U46(isNeList(V2))) ACTIVE(U51(tt,V1,V2)) -> MARK(U52(isPalListKind(V1),V1,V2)) ACTIVE(U52(tt,V1,V2)) -> MARK(U53(isPalListKind(V2),V1,V2)) ACTIVE(U53(tt,V1,V2)) -> MARK(U54(isPalListKind(V2),V1,V2)) ACTIVE(U54(tt,V1,V2)) -> MARK(U55(isNeList(V1),V2)) ACTIVE(U55(tt,V2)) -> MARK(U56(isList(V2))) ACTIVE(U61(tt,V)) -> MARK(U62(isPalListKind(V),V)) ACTIVE(U62(tt,V)) -> MARK(U63(isQid(V))) ACTIVE(U71(tt,I,P)) -> MARK(U72(isPalListKind(I),P)) ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U43(tt,V1,V2)) -> MARK(U44(isPalListKind(V2),V1,V2)) ACTIVE(U44(tt,V1,V2)) -> MARK(U45(isList(V1),V2)) ACTIVE(U45(tt,V2)) -> MARK(U46(isNeList(V2))) ACTIVE(U51(tt,V1,V2)) -> MARK(U52(isPalListKind(V1),V1,V2)) ACTIVE(U52(tt,V1,V2)) -> MARK(U53(isPalListKind(V2),V1,V2)) ACTIVE(U53(tt,V1,V2)) -> MARK(U54(isPalListKind(V2),V1,V2)) ACTIVE(U54(tt,V1,V2)) -> MARK(U55(isNeList(V1),V2)) ACTIVE(U55(tt,V2)) -> MARK(U56(isList(V2))) ACTIVE(U61(tt,V)) -> MARK(U62(isPalListKind(V),V)) ACTIVE(U62(tt,V)) -> MARK(U63(isQid(V))) ACTIVE(U71(tt,I,P)) -> MARK(U72(isPalListKind(I),P)) ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U43(tt,V1,V2)) -> MARK(U44(isPalListKind(V2),V1,V2)) ACTIVE(U44(tt,V1,V2)) -> MARK(U45(isList(V1),V2)) ACTIVE(U45(tt,V2)) -> MARK(U46(isNeList(V2))) ACTIVE(U51(tt,V1,V2)) -> MARK(U52(isPalListKind(V1),V1,V2)) ACTIVE(U52(tt,V1,V2)) -> MARK(U53(isPalListKind(V2),V1,V2)) ACTIVE(U53(tt,V1,V2)) -> MARK(U54(isPalListKind(V2),V1,V2)) ACTIVE(U54(tt,V1,V2)) -> MARK(U55(isNeList(V1),V2)) ACTIVE(U55(tt,V2)) -> MARK(U56(isList(V2))) ACTIVE(U61(tt,V)) -> MARK(U62(isPalListKind(V),V)) ACTIVE(U62(tt,V)) -> MARK(U63(isQid(V))) ACTIVE(U71(tt,I,P)) -> MARK(U72(isPalListKind(I),P)) ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = X1 + 2.X2 [U12](X1,X2) = X1 + 2.X2 [U13](X) = X [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 1 [U22](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 1 [U23](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 1 [U24](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U25](X1,X2) = X1 + 2.X2 + 2 [U26](X) = X + 1 [U31](X1,X2) = X1 [U32](X1,X2) = X1 [U33](X) = X [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U43](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U44](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 1 [U45](X1,X2) = X1 + 2.X2 + 1 [U46](X) = X + 1 [U51](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U52](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 [U53](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U54](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U55](X1,X2) = X1 + 2.X2 + 2 [U56](X) = X + 2 [U61](X1,X2) = X1 + X2 [U62](X1,X2) = X1 + X2 [U63](X) = X [U71](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U72](X1,X2) = 2.X1 + 2.X2 + 2 [U73](X1,X2) = 2.X1 + 2 [U74](X) = 2.X [U81](X1,X2) = X1 + X2 [U82](X1,X2) = X1 + X2 [U83](X) = X [U91](X1,X2) = X1 [U92](X) = X [__](X1,X2) = 2.X1 + X2 + 2 [active](X) = X [isList](X) = 2.X + 2 [isNeList](X) = 2.X + 2 [isNePal](X) = X + 2 [isPal](X) = X + 2 [isPalListKind](X) = 2 [isQid](X) = 2 [mark](X) = X [a] = 2 [e] = 0 [i] = 2 [nil] = 2 [o] = 2 [tt] = 2 [u] = 2 [ACTIVE](X) = 2.X + 2 [MARK](X) = 2.X + 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U44(tt,V1,V2)) -> MARK(U45(isList(V1),V2)) ACTIVE(U45(tt,V2)) -> MARK(U46(isNeList(V2))) ACTIVE(U51(tt,V1,V2)) -> MARK(U52(isPalListKind(V1),V1,V2)) ACTIVE(U52(tt,V1,V2)) -> MARK(U53(isPalListKind(V2),V1,V2)) ACTIVE(U53(tt,V1,V2)) -> MARK(U54(isPalListKind(V2),V1,V2)) ACTIVE(U54(tt,V1,V2)) -> MARK(U55(isNeList(V1),V2)) ACTIVE(U55(tt,V2)) -> MARK(U56(isList(V2))) ACTIVE(U61(tt,V)) -> MARK(U62(isPalListKind(V),V)) ACTIVE(U62(tt,V)) -> MARK(U63(isQid(V))) ACTIVE(U71(tt,I,P)) -> MARK(U72(isPalListKind(I),P)) ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U44(tt,V1,V2)) -> MARK(U45(isList(V1),V2)) ACTIVE(U45(tt,V2)) -> MARK(U46(isNeList(V2))) ACTIVE(U51(tt,V1,V2)) -> MARK(U52(isPalListKind(V1),V1,V2)) ACTIVE(U52(tt,V1,V2)) -> MARK(U53(isPalListKind(V2),V1,V2)) ACTIVE(U53(tt,V1,V2)) -> MARK(U54(isPalListKind(V2),V1,V2)) ACTIVE(U54(tt,V1,V2)) -> MARK(U55(isNeList(V1),V2)) ACTIVE(U55(tt,V2)) -> MARK(U56(isList(V2))) ACTIVE(U61(tt,V)) -> MARK(U62(isPalListKind(V),V)) ACTIVE(U62(tt,V)) -> MARK(U63(isQid(V))) ACTIVE(U71(tt,I,P)) -> MARK(U72(isPalListKind(I),P)) ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U44(tt,V1,V2)) -> MARK(U45(isList(V1),V2)) ACTIVE(U45(tt,V2)) -> MARK(U46(isNeList(V2))) ACTIVE(U51(tt,V1,V2)) -> MARK(U52(isPalListKind(V1),V1,V2)) ACTIVE(U52(tt,V1,V2)) -> MARK(U53(isPalListKind(V2),V1,V2)) ACTIVE(U53(tt,V1,V2)) -> MARK(U54(isPalListKind(V2),V1,V2)) ACTIVE(U54(tt,V1,V2)) -> MARK(U55(isNeList(V1),V2)) ACTIVE(U55(tt,V2)) -> MARK(U56(isList(V2))) ACTIVE(U61(tt,V)) -> MARK(U62(isPalListKind(V),V)) ACTIVE(U62(tt,V)) -> MARK(U63(isQid(V))) ACTIVE(U71(tt,I,P)) -> MARK(U72(isPalListKind(I),P)) ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = X1 + 2.X2 [U12](X1,X2) = X1 + 2.X2 [U13](X) = X [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U22](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U23](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U24](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U25](X1,X2) = X1 + 2.X2 + 2 [U26](X) = X + 2 [U31](X1,X2) = X1 + 2.X2 [U32](X1,X2) = X1 + 2.X2 [U33](X) = X [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U43](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U44](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U45](X1,X2) = X1 + 2.X2 + 2 [U46](X) = X + 2 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U52](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U53](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U54](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U55](X1,X2) = X1 + 2.X2 + 2 [U56](X) = X + 2 [U61](X1,X2) = X1 + 2.X2 [U62](X1,X2) = X1 + 2.X2 [U63](X) = X [U71](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U72](X1,X2) = X1 + 2.X2 + 2 [U73](X1,X2) = X1 + 1 [U74](X) = X + 1 [U81](X1,X2) = X1 + 2.X2 [U82](X1,X2) = X1 + 2.X2 [U83](X) = X [U91](X1,X2) = X1 [U92](X) = X [__](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 [isPalListKind](X) = 2 [isQid](X) = 2.X + 2 [mark](X) = X [a] = 2 [e] = 2 [i] = 2 [nil] = 0 [o] = 2 [tt] = 2 [u] = 2 [ACTIVE](X) = 2.X [MARK](X) = 2.X Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U45(tt,V2)) -> MARK(U46(isNeList(V2))) ACTIVE(U51(tt,V1,V2)) -> MARK(U52(isPalListKind(V1),V1,V2)) ACTIVE(U52(tt,V1,V2)) -> MARK(U53(isPalListKind(V2),V1,V2)) ACTIVE(U53(tt,V1,V2)) -> MARK(U54(isPalListKind(V2),V1,V2)) ACTIVE(U54(tt,V1,V2)) -> MARK(U55(isNeList(V1),V2)) ACTIVE(U55(tt,V2)) -> MARK(U56(isList(V2))) ACTIVE(U61(tt,V)) -> MARK(U62(isPalListKind(V),V)) ACTIVE(U62(tt,V)) -> MARK(U63(isQid(V))) ACTIVE(U71(tt,I,P)) -> MARK(U72(isPalListKind(I),P)) ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U45(tt,V2)) -> MARK(U46(isNeList(V2))) ACTIVE(U51(tt,V1,V2)) -> MARK(U52(isPalListKind(V1),V1,V2)) ACTIVE(U52(tt,V1,V2)) -> MARK(U53(isPalListKind(V2),V1,V2)) ACTIVE(U53(tt,V1,V2)) -> MARK(U54(isPalListKind(V2),V1,V2)) ACTIVE(U54(tt,V1,V2)) -> MARK(U55(isNeList(V1),V2)) ACTIVE(U55(tt,V2)) -> MARK(U56(isList(V2))) ACTIVE(U61(tt,V)) -> MARK(U62(isPalListKind(V),V)) ACTIVE(U62(tt,V)) -> MARK(U63(isQid(V))) ACTIVE(U71(tt,I,P)) -> MARK(U72(isPalListKind(I),P)) ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U45(tt,V2)) -> MARK(U46(isNeList(V2))) ACTIVE(U51(tt,V1,V2)) -> MARK(U52(isPalListKind(V1),V1,V2)) ACTIVE(U52(tt,V1,V2)) -> MARK(U53(isPalListKind(V2),V1,V2)) ACTIVE(U53(tt,V1,V2)) -> MARK(U54(isPalListKind(V2),V1,V2)) ACTIVE(U54(tt,V1,V2)) -> MARK(U55(isNeList(V1),V2)) ACTIVE(U55(tt,V2)) -> MARK(U56(isList(V2))) ACTIVE(U61(tt,V)) -> MARK(U62(isPalListKind(V),V)) ACTIVE(U62(tt,V)) -> MARK(U63(isQid(V))) ACTIVE(U71(tt,I,P)) -> MARK(U72(isPalListKind(I),P)) ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = X1 + 2.X2 [U12](X1,X2) = X1 + 2.X2 [U13](X) = X [U21](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U22](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U23](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 [U24](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U25](X1,X2) = X1 + 2.X2 + 2 [U26](X) = X + 2 [U31](X1,X2) = X1 + 2.X2 [U32](X1,X2) = X1 + 2.X2 [U33](X) = X [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U43](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U44](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U45](X1,X2) = X1 + 2.X2 + 2 [U46](X) = X + 1 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U52](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U53](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 [U54](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 1 [U55](X1,X2) = X1 + 2.X2 [U56](X) = X [U61](X1,X2) = X1 + 2.X2 [U62](X1,X2) = X1 + X2 [U63](X) = X [U71](X1,X2,X3) = 2.X1 + 2.X3 + 2 [U72](X1,X2) = X1 + 2.X2 + 2 [U73](X1,X2) = X1 [U74](X) = X [U81](X1,X2) = X1 + 2.X2 [U82](X1,X2) = X1 + 2.X2 [U83](X) = X [U91](X1,X2) = X1 [U92](X) = X [__](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 [isPalListKind](X) = 2 [isQid](X) = 2 [mark](X) = X [a] = 1 [e] = 0 [i] = 2 [nil] = 2 [o] = 0 [tt] = 2 [u] = 2 [ACTIVE](X) = 2.X + 2 [MARK](X) = 2.X + 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U51(tt,V1,V2)) -> MARK(U52(isPalListKind(V1),V1,V2)) ACTIVE(U52(tt,V1,V2)) -> MARK(U53(isPalListKind(V2),V1,V2)) ACTIVE(U53(tt,V1,V2)) -> MARK(U54(isPalListKind(V2),V1,V2)) ACTIVE(U54(tt,V1,V2)) -> MARK(U55(isNeList(V1),V2)) ACTIVE(U55(tt,V2)) -> MARK(U56(isList(V2))) ACTIVE(U61(tt,V)) -> MARK(U62(isPalListKind(V),V)) ACTIVE(U62(tt,V)) -> MARK(U63(isQid(V))) ACTIVE(U71(tt,I,P)) -> MARK(U72(isPalListKind(I),P)) ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U51(tt,V1,V2)) -> MARK(U52(isPalListKind(V1),V1,V2)) ACTIVE(U52(tt,V1,V2)) -> MARK(U53(isPalListKind(V2),V1,V2)) ACTIVE(U53(tt,V1,V2)) -> MARK(U54(isPalListKind(V2),V1,V2)) ACTIVE(U54(tt,V1,V2)) -> MARK(U55(isNeList(V1),V2)) ACTIVE(U55(tt,V2)) -> MARK(U56(isList(V2))) ACTIVE(U61(tt,V)) -> MARK(U62(isPalListKind(V),V)) ACTIVE(U62(tt,V)) -> MARK(U63(isQid(V))) ACTIVE(U71(tt,I,P)) -> MARK(U72(isPalListKind(I),P)) ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U51(tt,V1,V2)) -> MARK(U52(isPalListKind(V1),V1,V2)) ACTIVE(U52(tt,V1,V2)) -> MARK(U53(isPalListKind(V2),V1,V2)) ACTIVE(U53(tt,V1,V2)) -> MARK(U54(isPalListKind(V2),V1,V2)) ACTIVE(U54(tt,V1,V2)) -> MARK(U55(isNeList(V1),V2)) ACTIVE(U55(tt,V2)) -> MARK(U56(isList(V2))) ACTIVE(U61(tt,V)) -> MARK(U62(isPalListKind(V),V)) ACTIVE(U62(tt,V)) -> MARK(U63(isQid(V))) ACTIVE(U71(tt,I,P)) -> MARK(U72(isPalListKind(I),P)) ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = X1 + 2.X2 [U12](X1,X2) = X1 + 2.X2 [U13](X) = X [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U22](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 1 [U23](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 [U24](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 [U25](X1,X2) = X1 + 2.X2 + 2 [U26](X) = X + 2 [U31](X1,X2) = X1 + 2.X2 [U32](X1,X2) = X1 + 2.X2 [U33](X) = X [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 1 [U43](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U44](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U45](X1,X2) = X1 + 2.X2 + 2 [U46](X) = X + 2 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U52](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U53](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U54](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U55](X1,X2) = X1 + 2.X2 + 2 [U56](X) = X + 2 [U61](X1,X2) = X1 + 2.X2 [U62](X1,X2) = X1 + 2.X2 [U63](X) = X [U71](X1,X2,X3) = 2.X1 + 2.X3 + 2 [U72](X1,X2) = 2.X1 + 2.X2 + 2 [U73](X1,X2) = X1 + 2 [U74](X) = X + 2 [U81](X1,X2) = X1 + 2.X2 [U82](X1,X2) = X1 + 2.X2 [U83](X) = X [U91](X1,X2) = X1 [U92](X) = X [__](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 [isPalListKind](X) = 2 [isQid](X) = 2.X + 2 [mark](X) = X [a] = 2 [e] = 1 [i] = 1 [nil] = 2 [o] = 0 [tt] = 2 [u] = 2 [ACTIVE](X) = 2.X + 2 [MARK](X) = 2.X + 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U52(tt,V1,V2)) -> MARK(U53(isPalListKind(V2),V1,V2)) ACTIVE(U53(tt,V1,V2)) -> MARK(U54(isPalListKind(V2),V1,V2)) ACTIVE(U54(tt,V1,V2)) -> MARK(U55(isNeList(V1),V2)) ACTIVE(U55(tt,V2)) -> MARK(U56(isList(V2))) ACTIVE(U61(tt,V)) -> MARK(U62(isPalListKind(V),V)) ACTIVE(U62(tt,V)) -> MARK(U63(isQid(V))) ACTIVE(U71(tt,I,P)) -> MARK(U72(isPalListKind(I),P)) ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U52(tt,V1,V2)) -> MARK(U53(isPalListKind(V2),V1,V2)) ACTIVE(U53(tt,V1,V2)) -> MARK(U54(isPalListKind(V2),V1,V2)) ACTIVE(U54(tt,V1,V2)) -> MARK(U55(isNeList(V1),V2)) ACTIVE(U55(tt,V2)) -> MARK(U56(isList(V2))) ACTIVE(U61(tt,V)) -> MARK(U62(isPalListKind(V),V)) ACTIVE(U62(tt,V)) -> MARK(U63(isQid(V))) ACTIVE(U71(tt,I,P)) -> MARK(U72(isPalListKind(I),P)) ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U52(tt,V1,V2)) -> MARK(U53(isPalListKind(V2),V1,V2)) ACTIVE(U53(tt,V1,V2)) -> MARK(U54(isPalListKind(V2),V1,V2)) ACTIVE(U54(tt,V1,V2)) -> MARK(U55(isNeList(V1),V2)) ACTIVE(U55(tt,V2)) -> MARK(U56(isList(V2))) ACTIVE(U61(tt,V)) -> MARK(U62(isPalListKind(V),V)) ACTIVE(U62(tt,V)) -> MARK(U63(isQid(V))) ACTIVE(U71(tt,I,P)) -> MARK(U72(isPalListKind(I),P)) ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = X1 + 2.X2 [U12](X1,X2) = X1 + 2.X2 [U13](X) = X [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U22](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 [U23](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U24](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 [U25](X1,X2) = X1 + 2.X2 + 2 [U26](X) = X + 2 [U31](X1,X2) = X1 + 2.X2 [U32](X1,X2) = X1 + 2.X2 [U33](X) = X [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U43](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U44](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U45](X1,X2) = X1 + 2.X2 + 2 [U46](X) = X + 2 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U52](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U53](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U54](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U55](X1,X2) = X1 + 2.X2 + 1 [U56](X) = X [U61](X1,X2) = X1 + X2 [U62](X1,X2) = X1 + X2 [U63](X) = X [U71](X1,X2,X3) = 2.X1 + 2.X3 + 2 [U72](X1,X2) = X1 + 2.X2 + 2 [U73](X1,X2) = X1 + 2 [U74](X) = X + 2 [U81](X1,X2) = X1 + 2.X2 [U82](X1,X2) = X1 + 2.X2 [U83](X) = X [U91](X1,X2) = X1 [U92](X) = X [__](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 [isPalListKind](X) = 2 [isQid](X) = 2 [mark](X) = X [a] = 1 [e] = 1 [i] = 1 [nil] = 1 [o] = 2 [tt] = 2 [u] = 1 [ACTIVE](X) = 2.X + 2 [MARK](X) = 2.X + 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U53(tt,V1,V2)) -> MARK(U54(isPalListKind(V2),V1,V2)) ACTIVE(U54(tt,V1,V2)) -> MARK(U55(isNeList(V1),V2)) ACTIVE(U55(tt,V2)) -> MARK(U56(isList(V2))) ACTIVE(U61(tt,V)) -> MARK(U62(isPalListKind(V),V)) ACTIVE(U62(tt,V)) -> MARK(U63(isQid(V))) ACTIVE(U71(tt,I,P)) -> MARK(U72(isPalListKind(I),P)) ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U53(tt,V1,V2)) -> MARK(U54(isPalListKind(V2),V1,V2)) ACTIVE(U54(tt,V1,V2)) -> MARK(U55(isNeList(V1),V2)) ACTIVE(U55(tt,V2)) -> MARK(U56(isList(V2))) ACTIVE(U61(tt,V)) -> MARK(U62(isPalListKind(V),V)) ACTIVE(U62(tt,V)) -> MARK(U63(isQid(V))) ACTIVE(U71(tt,I,P)) -> MARK(U72(isPalListKind(I),P)) ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U53(tt,V1,V2)) -> MARK(U54(isPalListKind(V2),V1,V2)) ACTIVE(U54(tt,V1,V2)) -> MARK(U55(isNeList(V1),V2)) ACTIVE(U55(tt,V2)) -> MARK(U56(isList(V2))) ACTIVE(U61(tt,V)) -> MARK(U62(isPalListKind(V),V)) ACTIVE(U62(tt,V)) -> MARK(U63(isQid(V))) ACTIVE(U71(tt,I,P)) -> MARK(U72(isPalListKind(I),P)) ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = X1 + 2.X2 [U12](X1,X2) = X1 + 2.X2 [U13](X) = X [U21](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U22](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U23](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 [U24](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U25](X1,X2) = X1 + 2.X2 + 2 [U26](X) = X + 2 [U31](X1,X2) = X1 + 2.X2 [U32](X1,X2) = X1 + 2.X2 [U33](X) = 2.X [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U43](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U44](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U45](X1,X2) = X1 + 2.X2 + 2 [U46](X) = X + 1 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U52](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U53](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U54](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 1 [U55](X1,X2) = X1 + 2.X2 + 1 [U56](X) = X + 1 [U61](X1,X2) = X1 + 2.X2 [U62](X1,X2) = X1 + 2.X2 [U63](X) = 2.X [U71](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U72](X1,X2) = 2.X1 + 2.X2 + 2 [U73](X1,X2) = X1 + 2 [U74](X) = 2.X [U81](X1,X2) = X1 + 2.X2 [U82](X1,X2) = X1 + 2.X2 [U83](X) = X [U91](X1,X2) = X1 [U92](X) = X [__](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 [isPalListKind](X) = 2 [isQid](X) = X + 1 [mark](X) = X [a] = 2 [e] = 2 [i] = 1 [nil] = 2 [o] = 2 [tt] = 2 [u] = 2 [ACTIVE](X) = 2.X + 2 [MARK](X) = 2.X + 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U54(tt,V1,V2)) -> MARK(U55(isNeList(V1),V2)) ACTIVE(U55(tt,V2)) -> MARK(U56(isList(V2))) ACTIVE(U61(tt,V)) -> MARK(U62(isPalListKind(V),V)) ACTIVE(U62(tt,V)) -> MARK(U63(isQid(V))) ACTIVE(U71(tt,I,P)) -> MARK(U72(isPalListKind(I),P)) ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U54(tt,V1,V2)) -> MARK(U55(isNeList(V1),V2)) ACTIVE(U55(tt,V2)) -> MARK(U56(isList(V2))) ACTIVE(U61(tt,V)) -> MARK(U62(isPalListKind(V),V)) ACTIVE(U62(tt,V)) -> MARK(U63(isQid(V))) ACTIVE(U71(tt,I,P)) -> MARK(U72(isPalListKind(I),P)) ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U54(tt,V1,V2)) -> MARK(U55(isNeList(V1),V2)) ACTIVE(U55(tt,V2)) -> MARK(U56(isList(V2))) ACTIVE(U61(tt,V)) -> MARK(U62(isPalListKind(V),V)) ACTIVE(U62(tt,V)) -> MARK(U63(isQid(V))) ACTIVE(U71(tt,I,P)) -> MARK(U72(isPalListKind(I),P)) ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = X1 + 2.X2 [U12](X1,X2) = X1 + 2.X2 [U13](X) = X [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U22](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U23](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U24](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U25](X1,X2) = X1 + 2.X2 + 2 [U26](X) = X + 2 [U31](X1,X2) = X1 + 2.X2 [U32](X1,X2) = X1 + X2 [U33](X) = X [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U43](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U44](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U45](X1,X2) = X1 + 2.X2 + 2 [U46](X) = X + 2 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U52](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U53](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U54](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 [U55](X1,X2) = X1 + 2.X2 + 1 [U56](X) = X [U61](X1,X2) = X1 + 2.X2 [U62](X1,X2) = X1 + 2.X2 [U63](X) = X [U71](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U72](X1,X2) = X1 + 2.X2 + 2 [U73](X1,X2) = X1 + 2 [U74](X) = X + 1 [U81](X1,X2) = X1 + 2.X2 [U82](X1,X2) = X1 + 2.X2 [U83](X) = X [U91](X1,X2) = X1 [U92](X) = X [__](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 [isPalListKind](X) = 2 [isQid](X) = 2 [mark](X) = X [a] = 1 [e] = 0 [i] = 0 [nil] = 2 [o] = 0 [tt] = 2 [u] = 1 [ACTIVE](X) = 2.X + 2 [MARK](X) = 2.X + 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U55(tt,V2)) -> MARK(U56(isList(V2))) ACTIVE(U61(tt,V)) -> MARK(U62(isPalListKind(V),V)) ACTIVE(U62(tt,V)) -> MARK(U63(isQid(V))) ACTIVE(U71(tt,I,P)) -> MARK(U72(isPalListKind(I),P)) ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U55(tt,V2)) -> MARK(U56(isList(V2))) ACTIVE(U61(tt,V)) -> MARK(U62(isPalListKind(V),V)) ACTIVE(U62(tt,V)) -> MARK(U63(isQid(V))) ACTIVE(U71(tt,I,P)) -> MARK(U72(isPalListKind(I),P)) ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U55(tt,V2)) -> MARK(U56(isList(V2))) ACTIVE(U61(tt,V)) -> MARK(U62(isPalListKind(V),V)) ACTIVE(U62(tt,V)) -> MARK(U63(isQid(V))) ACTIVE(U71(tt,I,P)) -> MARK(U72(isPalListKind(I),P)) ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = X1 + X2 [U12](X1,X2) = X1 + X2 [U13](X) = X [U21](X1,X2,X3) = 2.X1 + 2.X2 + X3 [U22](X1,X2,X3) = X1 + 2.X2 + X3 + 2 [U23](X1,X2,X3) = X1 + 2.X2 + X3 + 2 [U24](X1,X2,X3) = 2.X1 + 2.X2 + X3 [U25](X1,X2) = 2.X1 + X2 [U26](X) = X + 1 [U31](X1,X2) = X1 + X2 [U32](X1,X2) = X1 + X2 [U33](X) = X + 2 [U41](X1,X2,X3) = X1 + 2.X2 + X3 + 2 [U42](X1,X2,X3) = X1 + 2.X2 + X3 + 2 [U43](X1,X2,X3) = 2.X1 + 2.X2 + X3 [U44](X1,X2,X3) = X1 + X2 + X3 + 2 [U45](X1,X2) = X1 + X2 + 2 [U46](X) = X + 2 [U51](X1,X2,X3) = X1 + 2.X2 + X3 + 2 [U52](X1,X2,X3) = 2.X1 + 2.X2 + X3 [U53](X1,X2,X3) = X1 + 2.X2 + X3 + 2 [U54](X1,X2,X3) = 2.X1 + 2.X2 + X3 [U55](X1,X2) = X1 + X2 + 2 [U56](X) = X + 1 [U61](X1,X2) = X1 + X2 [U62](X1,X2) = X1 + X2 [U63](X) = X + 2 [U71](X1,X2,X3) = 2.X1 + X2 + 2.X3 + 2 [U72](X1,X2) = 2.X1 + 2.X2 + 2 [U73](X1,X2) = 2.X1 + 2 [U74](X) = X [U81](X1,X2) = X1 + X2 [U82](X1,X2) = X1 + X2 [U83](X) = X [U91](X1,X2) = X1 [U92](X) = X [__](X1,X2) = 2.X1 + X2 + 2 [active](X) = X [isList](X) = X + 2 [isNeList](X) = X + 2 [isNePal](X) = X + 2 [isPal](X) = X + 2 [isPalListKind](X) = 2 [isQid](X) = X [mark](X) = X [a] = 2 [e] = 2 [i] = 2 [nil] = 2 [o] = 2 [tt] = 2 [u] = 2 [ACTIVE](X) = 2.X + 1 [MARK](X) = 2.X + 1 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U61(tt,V)) -> MARK(U62(isPalListKind(V),V)) ACTIVE(U62(tt,V)) -> MARK(U63(isQid(V))) ACTIVE(U71(tt,I,P)) -> MARK(U72(isPalListKind(I),P)) ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U61(tt,V)) -> MARK(U62(isPalListKind(V),V)) ACTIVE(U62(tt,V)) -> MARK(U63(isQid(V))) ACTIVE(U71(tt,I,P)) -> MARK(U72(isPalListKind(I),P)) ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U61(tt,V)) -> MARK(U62(isPalListKind(V),V)) ACTIVE(U62(tt,V)) -> MARK(U63(isQid(V))) ACTIVE(U71(tt,I,P)) -> MARK(U72(isPalListKind(I),P)) ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = 2.X1 + 2.X2 [U12](X1,X2) = X1 + 2.X2 + 1 [U13](X) = X [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U22](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U23](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U24](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U25](X1,X2) = X1 + 2.X2 + 2 [U26](X) = X + 1 [U31](X1,X2) = 2.X1 + 2.X2 [U32](X1,X2) = 2.X1 + X2 [U33](X) = 2.X [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U43](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U44](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U45](X1,X2) = X1 + 2.X2 + 2 [U46](X) = X + 1 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U52](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U53](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U54](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U55](X1,X2) = X1 + 2.X2 + 2 [U56](X) = X + 1 [U61](X1,X2) = 2.X1 [U62](X1,X2) = X1 [U63](X) = X [U71](X1,X2,X3) = 2.X1 + X2 + 2.X3 + 2 [U72](X1,X2) = 2.X1 + 2.X2 + 2 [U73](X1,X2) = X1 + 2 [U74](X) = X + 2 [U81](X1,X2) = 2.X1 + 2.X2 [U82](X1,X2) = X1 + 2.X2 + 1 [U83](X) = X [U91](X1,X2) = X1 [U92](X) = X [__](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 [isPalListKind](X) = 1 [isQid](X) = 1 [mark](X) = X [a] = 2 [e] = 1 [i] = 1 [nil] = 2 [o] = 0 [tt] = 1 [u] = 1 [ACTIVE](X) = 2.X + 2 [MARK](X) = 2.X + 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U62(tt,V)) -> MARK(U63(isQid(V))) ACTIVE(U71(tt,I,P)) -> MARK(U72(isPalListKind(I),P)) ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U62(tt,V)) -> MARK(U63(isQid(V))) ACTIVE(U71(tt,I,P)) -> MARK(U72(isPalListKind(I),P)) ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U62(tt,V)) -> MARK(U63(isQid(V))) ACTIVE(U71(tt,I,P)) -> MARK(U72(isPalListKind(I),P)) ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = X1 + 2.X2 [U12](X1,X2) = X1 + 2.X2 [U13](X) = X [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U22](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U23](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U24](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U25](X1,X2) = X1 + 2.X2 + 2 [U26](X) = X [U31](X1,X2) = X1 + 2.X2 [U32](X1,X2) = X1 + 2.X2 [U33](X) = 2.X + 2 [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U43](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U44](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U45](X1,X2) = X1 + 2.X2 + 2 [U46](X) = X + 2 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U52](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U53](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 [U54](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U55](X1,X2) = X1 + 2.X2 + 1 [U56](X) = X + 1 [U61](X1,X2) = X1 + X2 [U62](X1,X2) = X1 + X2 [U63](X) = X + 1 [U71](X1,X2,X3) = 2.X1 + 2.X3 + 2 [U72](X1,X2) = 2.X1 + 2.X2 + 2 [U73](X1,X2) = X1 + 2 [U74](X) = X [U81](X1,X2) = X1 + 2.X2 [U82](X1,X2) = X1 + 2.X2 [U83](X) = X [U91](X1,X2) = X1 [U92](X) = X [__](X1,X2) = 2.X1 + X2 + 2 [active](X) = X [isList](X) = 2.X + 2 [isNeList](X) = 2.X + 2 [isNePal](X) = X + 2 [isPal](X) = 2.X + 2 [isPalListKind](X) = 2 [isQid](X) = X [mark](X) = X [a] = 2 [e] = 2 [i] = 2 [nil] = 2 [o] = 2 [tt] = 2 [u] = 2 [ACTIVE](X) = 2.X + 2 [MARK](X) = 2.X + 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U71(tt,I,P)) -> MARK(U72(isPalListKind(I),P)) ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U71(tt,I,P)) -> MARK(U72(isPalListKind(I),P)) ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U71(tt,I,P)) -> MARK(U72(isPalListKind(I),P)) ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = X1 + 2.X2 [U12](X1,X2) = X1 + 2.X2 [U13](X) = X [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U22](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 [U23](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 [U24](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 [U25](X1,X2) = X1 + 2.X2 + 2 [U26](X) = X + 2 [U31](X1,X2) = X1 + 2.X2 [U32](X1,X2) = X1 + 2.X2 [U33](X) = X [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U43](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U44](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U45](X1,X2) = X1 + 2.X2 + 2 [U46](X) = X [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U52](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U53](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U54](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U55](X1,X2) = X1 + 2.X2 + 2 [U56](X) = X + 2 [U61](X1,X2) = X1 + 2.X2 [U62](X1,X2) = X1 + 2.X2 [U63](X) = X [U71](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U72](X1,X2) = X1 + 2.X2 + 1 [U73](X1,X2) = X1 + 1 [U74](X) = X + 1 [U81](X1,X2) = X1 + 2.X2 [U82](X1,X2) = X1 + 2.X2 [U83](X) = X [U91](X1,X2) = X1 [U92](X) = X [__](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 [isPalListKind](X) = 2 [isQid](X) = 2.X + 2 [mark](X) = X [a] = 2 [e] = 1 [i] = 1 [nil] = 0 [o] = 1 [tt] = 2 [u] = 2 [ACTIVE](X) = 2.X [MARK](X) = 2.X Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U72(tt,P)) -> MARK(U73(isPal(P),P)) ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = X1 + 2.X2 [U12](X1,X2) = X1 + 2.X2 [U13](X) = X [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U22](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U23](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U24](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U25](X1,X2) = X1 + 2.X2 + 2 [U26](X) = X + 2 [U31](X1,X2) = X1 + 2.X2 [U32](X1,X2) = X1 + 2.X2 [U33](X) = X [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U43](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U44](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U45](X1,X2) = X1 + 2.X2 + 2 [U46](X) = X + 1 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U52](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U53](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U54](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U55](X1,X2) = X1 + 2.X2 + 2 [U56](X) = X + 2 [U61](X1,X2) = X1 + 2.X2 [U62](X1,X2) = X1 + 2.X2 [U63](X) = X [U71](X1,X2,X3) = 2.X1 + 2.X3 + 2 [U72](X1,X2) = 2.X1 + 2.X2 + 2 [U73](X1,X2) = X1 + 2 [U74](X) = X + 2 [U81](X1,X2) = X1 + 2.X2 [U82](X1,X2) = X1 + 2.X2 [U83](X) = X [U91](X1,X2) = X1 [U92](X) = X [__](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 [isPalListKind](X) = 2 [isQid](X) = 2.X + 2 [mark](X) = X [a] = 2 [e] = 2 [i] = 0 [nil] = 0 [o] = 2 [tt] = 2 [u] = 2 [ACTIVE](X) = 2.X + 2 [MARK](X) = 2.X + 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U73(tt,P)) -> MARK(U74(isPalListKind(P))) ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = X1 + 2.X2 [U12](X1,X2) = X1 + 2.X2 [U13](X) = X [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U22](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U23](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U24](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 [U25](X1,X2) = X1 + 2.X2 + 2 [U26](X) = X + 1 [U31](X1,X2) = X1 + 2.X2 [U32](X1,X2) = X1 + 2.X2 [U33](X) = X + 2 [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U43](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U44](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U45](X1,X2) = X1 + 2.X2 + 2 [U46](X) = X + 2 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U52](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U53](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U54](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U55](X1,X2) = X1 + 2.X2 + 2 [U56](X) = X + 2 [U61](X1,X2) = X1 + 2.X2 [U62](X1,X2) = X1 + 2.X2 [U63](X) = X + 2 [U71](X1,X2,X3) = 2.X1 + X2 + 2.X3 + 2 [U72](X1,X2) = 2.X1 + 2.X2 + 2 [U73](X1,X2) = X1 + 2 [U74](X) = X + 1 [U81](X1,X2) = X1 + 2.X2 [U82](X1,X2) = X1 + 2.X2 [U83](X) = X [U91](X1,X2) = X1 [U92](X) = X [__](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 [isPalListKind](X) = 2 [isQid](X) = 2.X [mark](X) = X [a] = 2 [e] = 2 [i] = 2 [nil] = 1 [o] = 2 [tt] = 2 [u] = 2 [ACTIVE](X) = 2.X + 1 [MARK](X) = 2.X + 1 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U81(tt,V)) -> MARK(U82(isPalListKind(V),V)) ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = 2.X1 + 2.X2 + 1 [U12](X1,X2) = 2.X1 + 2.X2 + 1 [U13](X) = X [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U22](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U23](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U24](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U25](X1,X2) = X1 + 2.X2 + 1 [U26](X) = X [U31](X1,X2) = 2.X1 + 2.X2 + 1 [U32](X1,X2) = 2.X1 + 2.X2 + 1 [U33](X) = 2.X + 1 [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U43](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U44](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U45](X1,X2) = X1 + 2.X2 + 1 [U46](X) = X [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U52](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U53](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U54](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U55](X1,X2) = X1 + 2.X2 + 1 [U56](X) = X [U61](X1,X2) = 2.X1 + 2.X2 + 1 [U62](X1,X2) = 2.X1 + 2.X2 + 1 [U63](X) = 2.X + 1 [U71](X1,X2,X3) = 2.X1 + X2 + 2.X3 + 2 [U72](X1,X2) = 2.X1 + 2.X2 + 2 [U73](X1,X2) = X1 [U74](X) = 2.X [U81](X1,X2) = 2.X1 + 2.X2 + 2 [U82](X1,X2) = 2.X1 + 2.X2 + 1 [U83](X) = X [U91](X1,X2) = 2.X1 [U92](X) = 2.X [__](X1,X2) = 2.X1 + X2 + 2 [active](X) = X [isList](X) = 2.X + 1 [isNeList](X) = 2.X + 1 [isNePal](X) = 2.X + 1 [isPal](X) = 2.X + 2 [isPalListKind](X) = 0 [isQid](X) = 0 [mark](X) = X [a] = 0 [e] = 0 [i] = 2 [nil] = 2 [o] = 2 [tt] = 0 [u] = 2 [ACTIVE](X) = 2.X + 2 [MARK](X) = 2.X + 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U82(tt,V)) -> MARK(U83(isNePal(V))) ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = X1 + 2.X2 + 1 [U12](X1,X2) = X1 + 2.X2 + 1 [U13](X) = X [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U22](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U23](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U24](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U25](X1,X2) = X1 + 2.X2 + 2 [U26](X) = X + 1 [U31](X1,X2) = 2.X1 + 2.X2 [U32](X1,X2) = 2.X1 + 2.X2 [U33](X) = 2.X + 2 [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U43](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U44](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 1 [U45](X1,X2) = X1 + 2.X2 + 1 [U46](X) = X [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U52](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U53](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U54](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U55](X1,X2) = X1 + 2.X2 + 2 [U56](X) = X + 1 [U61](X1,X2) = X1 + 2.X2 [U62](X1,X2) = X1 + 2.X2 [U63](X) = 2.X [U71](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U72](X1,X2) = 2.X1 + 2.X2 + 2 [U73](X1,X2) = X1 + 2 [U74](X) = X + 2 [U81](X1,X2) = X1 + 2.X2 + 1 [U82](X1,X2) = X1 + 2.X2 + 1 [U83](X) = X [U91](X1,X2) = X1 [U92](X) = X [__](X1,X2) = 2.X1 + X2 + 2 [active](X) = X [isList](X) = 2.X + 2 [isNeList](X) = 2.X + 2 [isNePal](X) = 2.X + 1 [isPal](X) = 2.X + 2 [isPalListKind](X) = 1 [isQid](X) = X [mark](X) = X [a] = 2 [e] = 2 [i] = 1 [nil] = 2 [o] = 2 [tt] = 1 [u] = 1 [ACTIVE](X) = 2.X + 2 [MARK](X) = 2.X + 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = X1 + 2.X2 [U12](X1,X2) = X1 + 2.X2 [U13](X) = X [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U22](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U23](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U24](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U25](X1,X2) = X1 + 2.X2 + 2 [U26](X) = X + 2 [U31](X1,X2) = X1 + 2.X2 [U32](X1,X2) = X1 + 2.X2 [U33](X) = X [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U43](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 1 [U44](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U45](X1,X2) = X1 + 2.X2 + 2 [U46](X) = X + 2 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 1 [U52](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U53](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 [U54](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U55](X1,X2) = X1 + 2.X2 + 2 [U56](X) = X + 2 [U61](X1,X2) = X1 + 2.X2 [U62](X1,X2) = X1 + 2.X2 [U63](X) = X [U71](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 1 [U72](X1,X2) = 2.X1 + 2.X2 [U73](X1,X2) = X1 + 1 [U74](X) = X + 1 [U81](X1,X2) = X1 + 2.X2 [U82](X1,X2) = X1 + 2.X2 [U83](X) = X [U91](X1,X2) = X1 [U92](X) = X [__](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 [isPalListKind](X) = 2 [isQid](X) = 2.X + 2 [mark](X) = X [a] = 1 [e] = 2 [i] = 2 [nil] = 2 [o] = 0 [tt] = 2 [u] = 2 [ACTIVE](X) = 2.X + 2 [MARK](X) = 2.X + 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(nil,X)) -> MARK(X) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = X1 + 2.X2 [U12](X1,X2) = X1 + 2.X2 [U13](X) = X [U21](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U22](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U23](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 [U24](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U25](X1,X2) = X1 + 2.X2 + 2 [U26](X) = X + 2 [U31](X1,X2) = X1 + 2.X2 [U32](X1,X2) = X1 + 2.X2 [U33](X) = X [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U43](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U44](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U45](X1,X2) = X1 + 2.X2 + 2 [U46](X) = X + 2 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U52](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U53](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U54](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U55](X1,X2) = X1 + 2.X2 + 2 [U56](X) = X + 2 [U61](X1,X2) = X1 + 2.X2 [U62](X1,X2) = X1 + 2.X2 [U63](X) = X [U71](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U72](X1,X2) = 2.X1 + 2.X2 + 2 [U73](X1,X2) = X1 + 2 [U74](X) = 2.X [U81](X1,X2) = X1 + 2.X2 [U82](X1,X2) = X1 + 2.X2 [U83](X) = X [U91](X1,X2) = X1 [U92](X) = X [__](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 [isPalListKind](X) = 2 [isQid](X) = 2 [mark](X) = X [a] = 2 [e] = 2 [i] = 1 [nil] = 2 [o] = 0 [tt] = 2 [u] = 0 [ACTIVE](X) = 2.X + 2 [MARK](X) = 2.X + 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(__(X,nil)) -> MARK(X) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = X1 + 2.X2 [U12](X1,X2) = X1 + 2.X2 [U13](X) = X [U21](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U22](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 [U23](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 [U24](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U25](X1,X2) = X1 + 2.X2 + 2 [U26](X) = X + 2 [U31](X1,X2) = X1 + 2.X2 [U32](X1,X2) = X1 + X2 [U33](X) = X [U41](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U43](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U44](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U45](X1,X2) = X1 + 2.X2 + 2 [U46](X) = X + 2 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U52](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U53](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U54](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U55](X1,X2) = X1 + 2.X2 + 2 [U56](X) = X + 2 [U61](X1,X2) = X1 + X2 [U62](X1,X2) = X1 + X2 [U63](X) = X [U71](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U72](X1,X2) = 2.X1 + 2.X2 + 2 [U73](X1,X2) = 2.X1 + 2 [U74](X) = 2.X + 2 [U81](X1,X2) = X1 + X2 [U82](X1,X2) = X1 + X2 [U83](X) = X [U91](X1,X2) = X1 [U92](X) = X [__](X1,X2) = 2.X1 + X2 + 2 [active](X) = X [isList](X) = 2.X + 2 [isNeList](X) = 2.X + 2 [isNePal](X) = X + 2 [isPal](X) = X + 2 [isPalListKind](X) = 2 [isQid](X) = 2 [mark](X) = X [a] = 0 [e] = 2 [i] = 2 [nil] = 0 [o] = 0 [tt] = 2 [u] = 1 [ACTIVE](X) = 2.X [MARK](X) = 2.X Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isList(__(V1,V2))) -> MARK(U21(isPalListKind(V1),V1,V2)) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = X1 + 2.X2 [U12](X1,X2) = X1 + 2.X2 [U13](X) = X [U21](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U22](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 [U23](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 [U24](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U25](X1,X2) = X1 + 2.X2 + 2 [U26](X) = X + 2 [U31](X1,X2) = X1 + 2.X2 [U32](X1,X2) = X1 + 2.X2 [U33](X) = X [U41](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U43](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U44](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 [U45](X1,X2) = X1 + 2.X2 + 2 [U46](X) = X + 1 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U52](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U53](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U54](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U55](X1,X2) = X1 + 2.X2 + 2 [U56](X) = X + 2 [U61](X1,X2) = X1 + X2 [U62](X1,X2) = X1 + X2 [U63](X) = X [U71](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U72](X1,X2) = 2.X1 + 2.X2 + 2 [U73](X1,X2) = 2.X1 + 2 [U74](X) = 2.X + 1 [U81](X1,X2) = X1 + X2 [U82](X1,X2) = X1 + X2 [U83](X) = X [U91](X1,X2) = X1 [U92](X) = X [__](X1,X2) = 2.X1 + X2 + 2 [active](X) = X [isList](X) = 2.X + 2 [isNeList](X) = 2.X + 2 [isNePal](X) = X + 2 [isPal](X) = X + 2 [isPalListKind](X) = 2 [isQid](X) = 2 [mark](X) = X [a] = 0 [e] = 2 [i] = 0 [nil] = 2 [o] = 0 [tt] = 2 [u] = 0 [ACTIVE](X) = 2.X + 2 [MARK](X) = 2.X + 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isList(V)) -> MARK(U11(isPalListKind(V),V)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = X1 + 2.X2 [U12](X1,X2) = X1 + 2.X2 [U13](X) = X [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U22](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U23](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U24](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U25](X1,X2) = X1 + 2.X2 + 2 [U26](X) = X + 1 [U31](X1,X2) = X1 + 2.X2 [U32](X1,X2) = X1 + 2.X2 [U33](X) = X [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U43](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U44](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U45](X1,X2) = X1 + 2.X2 + 2 [U46](X) = X [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 [U52](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 [U53](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 [U54](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 [U55](X1,X2) = X1 + 2.X2 + 1 [U56](X) = X [U61](X1,X2) = 2.X1 + X2 [U62](X1,X2) = X1 + 1 [U63](X) = 2.X [U71](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U72](X1,X2) = 2.X1 + 2.X2 + 2 [U73](X1,X2) = X1 + 2 [U74](X) = X + 2 [U81](X1,X2) = X1 + 2.X2 + 1 [U82](X1,X2) = 2.X1 + 2.X2 [U83](X) = X [U91](X1,X2) = X1 [U92](X) = X [__](X1,X2) = 2.X1 + X2 + 2 [active](X) = X [isList](X) = 2.X + 2 [isNeList](X) = 2.X + 1 [isNePal](X) = 2.X + 2 [isPal](X) = 2.X + 2 [isPalListKind](X) = 1 [isQid](X) = 1 [mark](X) = X [a] = 2 [e] = 0 [i] = 2 [nil] = 1 [o] = 0 [tt] = 1 [u] = 0 [ACTIVE](X) = 2.X + 2 [MARK](X) = 2.X + 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isNeList(__(V1,V2))) -> MARK(U41(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = X1 + 2.X2 [U12](X1,X2) = X1 + 2.X2 [U13](X) = X [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U22](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 1 [U23](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 1 [U24](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U25](X1,X2) = X1 + 2.X2 + 2 [U26](X) = X + 1 [U31](X1,X2) = X1 + 2.X2 [U32](X1,X2) = X1 + 2.X2 [U33](X) = X + 2 [U41](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 [U43](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U44](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 [U45](X1,X2) = X1 + 2.X2 + 2 [U46](X) = X + 2 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U52](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U53](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U54](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U55](X1,X2) = X1 + 2.X2 + 2 [U56](X) = X + 1 [U61](X1,X2) = X1 + 2.X2 [U62](X1,X2) = X1 + 2.X2 [U63](X) = X + 2 [U71](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U72](X1,X2) = 2.X1 + 2.X2 + 2 [U73](X1,X2) = X1 + 2 [U74](X) = X + 2 [U81](X1,X2) = X1 + 2.X2 [U82](X1,X2) = X1 + 2.X2 [U83](X) = X [U91](X1,X2) = X1 [U92](X) = X [__](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 [isPalListKind](X) = 2 [isQid](X) = 2.X [mark](X) = X [a] = 2 [e] = 2 [i] = 1 [nil] = 1 [o] = 2 [tt] = 2 [u] = 2 [ACTIVE](X) = 2.X + 2 [MARK](X) = 2.X + 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isNeList(__(V1,V2))) -> MARK(U51(isPalListKind(V1),V1,V2)) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = X1 + 2.X2 [U12](X1,X2) = X1 + 2.X2 [U13](X) = X [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U22](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U23](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U24](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U25](X1,X2) = X1 + 2.X2 + 2 [U26](X) = X + 2 [U31](X1,X2) = X1 + 2.X2 [U32](X1,X2) = X1 + 2.X2 [U33](X) = X [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U43](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U44](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U45](X1,X2) = X1 + 2.X2 + 2 [U46](X) = X + 2 [U51](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U52](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 [U53](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U54](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U55](X1,X2) = X1 + 2.X2 + 2 [U56](X) = X + 2 [U61](X1,X2) = X1 + 2.X2 [U62](X1,X2) = X1 + 2.X2 [U63](X) = X [U71](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U72](X1,X2) = 2.X1 + 2.X2 + 2 [U73](X1,X2) = X1 + 2 [U74](X) = X + 2 [U81](X1,X2) = X1 + 2.X2 [U82](X1,X2) = X1 + 2.X2 [U83](X) = X [U91](X1,X2) = X1 [U92](X) = X [__](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 [isPalListKind](X) = 2 [isQid](X) = 2.X + 2 [mark](X) = X [a] = 2 [e] = 2 [i] = 2 [nil] = 2 [o] = 2 [tt] = 2 [u] = 2 [ACTIVE](X) = 2.X + 2 [MARK](X) = 2.X + 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isNeList(V)) -> MARK(U31(isPalListKind(V),V)) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = 2.X1 + 2.X2 [U12](X1,X2) = X1 + 2.X2 + 1 [U13](X) = X [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U22](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U23](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U24](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U25](X1,X2) = X1 + 2.X2 + 2 [U26](X) = X + 1 [U31](X1,X2) = X1 + 2.X2 [U32](X1,X2) = X1 + 2.X2 [U33](X) = 2.X + 1 [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U43](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U44](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U45](X1,X2) = X1 + 2.X2 + 2 [U46](X) = X + 1 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U52](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U53](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U54](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U55](X1,X2) = X1 + 2.X2 + 2 [U56](X) = X + 1 [U61](X1,X2) = X1 + 2.X2 + 1 [U62](X1,X2) = 2.X1 + 2.X2 [U63](X) = X + 2 [U71](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U72](X1,X2) = 2.X1 + 2.X2 + 2 [U73](X1,X2) = X1 + 2 [U74](X) = X + 2 [U81](X1,X2) = 2.X1 + 2.X2 [U82](X1,X2) = 2.X1 + 2.X2 [U83](X) = X [U91](X1,X2) = X1 [U92](X) = X [__](X1,X2) = 2.X1 + X2 + 1 [active](X) = X [isList](X) = 2.X + 2 [isNeList](X) = 2.X + 2 [isNePal](X) = 2.X + 2 [isPal](X) = 2.X + 2 [isPalListKind](X) = 1 [isQid](X) = X [mark](X) = X [a] = 2 [e] = 2 [i] = 1 [nil] = 0 [o] = 1 [tt] = 1 [u] = 2 [ACTIVE](X) = 2.X + 2 [MARK](X) = 2.X + 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(U71(isQid(I),I,P)) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = X1 + X2 [U12](X1,X2) = X1 + X2 [U13](X) = X [U21](X1,X2,X3) = 2.X1 + 2.X2 + X3 [U22](X1,X2,X3) = X1 + 2.X2 + X3 + 2 [U23](X1,X2,X3) = X1 + 2.X2 + X3 + 2 [U24](X1,X2,X3) = 2.X1 + 2.X2 + X3 [U25](X1,X2) = 2.X1 + X2 [U26](X) = X + 2 [U31](X1,X2) = X1 + X2 [U32](X1,X2) = X1 + X2 [U33](X) = X + 1 [U41](X1,X2,X3) = 2.X1 + 2.X2 + X3 [U42](X1,X2,X3) = X1 + 2.X2 + X3 + 2 [U43](X1,X2,X3) = 2.X1 + 2.X2 + X3 [U44](X1,X2,X3) = X1 + 2.X2 + X3 + 2 [U45](X1,X2) = X1 + X2 + 2 [U46](X) = X + 2 [U51](X1,X2,X3) = X1 + 2.X2 + X3 + 2 [U52](X1,X2,X3) = 2.X1 + 2.X2 + X3 [U53](X1,X2,X3) = X1 + 2.X2 + X3 + 2 [U54](X1,X2,X3) = X1 + X2 + X3 + 1 [U55](X1,X2) = X1 + X2 + 1 [U56](X) = X + 1 [U61](X1,X2) = X1 + X2 [U62](X1,X2) = X1 + X2 [U63](X) = X + 1 [U71](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U72](X1,X2) = 2.X1 + 2.X2 + 1 [U73](X1,X2) = X1 + 2 [U74](X) = 2.X [U81](X1,X2) = X1 + 2.X2 [U82](X1,X2) = X1 + 2.X2 [U83](X) = X [U91](X1,X2) = X1 [U92](X) = X [__](X1,X2) = 2.X1 + X2 + 2 [active](X) = X [isList](X) = X + 2 [isNeList](X) = X + 2 [isNePal](X) = 2.X + 2 [isPal](X) = 2.X + 2 [isPalListKind](X) = 2 [isQid](X) = X + 1 [mark](X) = X [a] = 2 [e] = 1 [i] = 2 [nil] = 2 [o] = 2 [tt] = 2 [u] = 1 [ACTIVE](X) = 2.X + 2 [MARK](X) = 2.X + 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isNePal(V)) -> MARK(U61(isPalListKind(V),V)) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = X1 + 2.X2 [U12](X1,X2) = X1 + 2.X2 [U13](X) = X [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U22](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U23](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U24](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U25](X1,X2) = X1 + 2.X2 + 2 [U26](X) = X + 2 [U31](X1,X2) = X1 + 2.X2 [U32](X1,X2) = X1 [U33](X) = X [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U43](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U44](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U45](X1,X2) = X1 + 2.X2 + 2 [U46](X) = X + 2 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U52](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U53](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U54](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U55](X1,X2) = X1 + 2.X2 + 2 [U56](X) = X + 1 [U61](X1,X2) = X1 + 2.X2 [U62](X1,X2) = X1 [U63](X) = X [U71](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U72](X1,X2) = 2.X1 + 2.X2 + 2 [U73](X1,X2) = X1 + 2 [U74](X) = X + 2 [U81](X1,X2) = X1 + 2.X2 + 1 [U82](X1,X2) = 2.X1 + 2.X2 [U83](X) = X [U91](X1,X2) = X1 [U92](X) = X [__](X1,X2) = 2.X1 + X2 + 2 [active](X) = X [isList](X) = 2.X + 1 [isNeList](X) = 2.X + 1 [isNePal](X) = 2.X + 2 [isPal](X) = 2.X + 2 [isPalListKind](X) = 1 [isQid](X) = 1 [mark](X) = X [a] = 0 [e] = 0 [i] = 2 [nil] = 2 [o] = 2 [tt] = 1 [u] = 2 [ACTIVE](X) = 2.X + 2 [MARK](X) = 2.X + 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPal(V)) -> MARK(U81(isPalListKind(V),V)) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = X1 + 2.X2 + 1 [U12](X1,X2) = X1 + 2.X2 + 1 [U13](X) = X [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U22](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U23](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U24](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U25](X1,X2) = X1 + 2.X2 + 2 [U26](X) = X + 1 [U31](X1,X2) = 2.X1 + X2 [U32](X1,X2) = 2.X1 + X2 [U33](X) = 2.X [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U43](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U44](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U45](X1,X2) = X1 + 2.X2 + 2 [U46](X) = X [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U52](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U53](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U54](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U55](X1,X2) = X1 + 2.X2 + 2 [U56](X) = X + 1 [U61](X1,X2) = X1 [U62](X1,X2) = X1 [U63](X) = X [U71](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U72](X1,X2) = 2.X1 + 2.X2 + 2 [U73](X1,X2) = X1 + 2 [U74](X) = X + 2 [U81](X1,X2) = X1 + 2.X2 [U82](X1,X2) = X1 + 2.X2 [U83](X) = X [U91](X1,X2) = X1 [U92](X) = X [__](X1,X2) = 2.X1 + X2 + 2 [active](X) = X [isList](X) = 2.X + 2 [isNeList](X) = 2.X + 2 [isNePal](X) = 2.X + 1 [isPal](X) = 2.X + 2 [isPalListKind](X) = 1 [isQid](X) = 1 [mark](X) = X [a] = 0 [e] = 2 [i] = 1 [nil] = 2 [o] = 2 [tt] = 1 [u] = 2 [ACTIVE](X) = 2.X + 2 [MARK](X) = 2.X + 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> ACTIVE(U11(mark(X1),X2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = 0 [U12](X1,X2) = 1 [U13](X) = 1 [U21](X1,X2,X3) = 0 [U22](X1,X2,X3) = 1 [U23](X1,X2,X3) = 1 [U24](X1,X2,X3) = 1 [U25](X1,X2) = 1 [U26](X) = 1 [U31](X1,X2) = 0 [U32](X1,X2) = 0 [U33](X) = 0 [U41](X1,X2,X3) = 1 [U42](X1,X2,X3) = 1 [U43](X1,X2,X3) = 0 [U44](X1,X2,X3) = 0 [U45](X1,X2) = 1 [U46](X) = 0 [U51](X1,X2,X3) = 1 [U52](X1,X2,X3) = 1 [U53](X1,X2,X3) = 0 [U54](X1,X2,X3) = 1 [U55](X1,X2) = 1 [U56](X) = 1 [U61](X1,X2) = 1 [U62](X1,X2) = 1 [U63](X) = 1 [U71](X1,X2,X3) = 1 [U72](X1,X2) = 1 [U73](X1,X2) = 0 [U74](X) = 1 [U81](X1,X2) = 1 [U82](X1,X2) = 0 [U83](X) = 1 [U91](X1,X2) = 1 [U92](X) = 1 [__](X1,X2) = 1 [active](X) = 2 [isList](X) = 0 [isNeList](X) = 1 [isNePal](X) = 1 [isPal](X) = 1 [isPalListKind](X) = 1 [isQid](X) = 1 [mark](X) = 2 [a] = 2 [e] = 2 [i] = 0 [nil] = 2 [o] = 0 [tt] = 0 [u] = 1 [ACTIVE](X) = 2.X [MARK](X) = 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U11(X1,X2)) -> MARK(X1) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = X1 + 2.X2 + 1 [U12](X1,X2) = X1 + 2.X2 + 1 [U13](X) = X [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U22](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U23](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U24](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U25](X1,X2) = X1 + 2.X2 + 2 [U26](X) = X [U31](X1,X2) = 2.X1 + 2.X2 [U32](X1,X2) = 2.X1 + 2.X2 [U33](X) = X [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U43](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U44](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U45](X1,X2) = X1 + 2.X2 + 2 [U46](X) = X + 1 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U52](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U53](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U54](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U55](X1,X2) = X1 + 2.X2 + 2 [U56](X) = X + 1 [U61](X1,X2) = X1 + 2.X2 + 1 [U62](X1,X2) = 2.X1 + 2.X2 [U63](X) = X [U71](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U72](X1,X2) = 2.X1 + 2.X2 + 2 [U73](X1,X2) = X1 + 2 [U74](X) = X + 2 [U81](X1,X2) = X1 + 2.X2 + 1 [U82](X1,X2) = 2.X1 + 2.X2 [U83](X) = X [U91](X1,X2) = X1 [U92](X) = X [__](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 [isPalListKind](X) = 1 [isQid](X) = 2.X + 2 [mark](X) = X [a] = 1 [e] = 1 [i] = 0 [nil] = 2 [o] = 2 [tt] = 1 [u] = 1 [ACTIVE](X) = 2.X + 2 [MARK](X) = 2.X + 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U12(X1,X2)) -> ACTIVE(U12(mark(X1),X2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = 2 [U12](X1,X2) = 0 [U13](X) = 1 [U21](X1,X2,X3) = 0 [U22](X1,X2,X3) = 0 [U23](X1,X2,X3) = 0 [U24](X1,X2,X3) = 0 [U25](X1,X2) = 0 [U26](X) = 1 [U31](X1,X2) = 1 [U32](X1,X2) = 0 [U33](X) = 1 [U41](X1,X2,X3) = 1 [U42](X1,X2,X3) = 1 [U43](X1,X2,X3) = 0 [U44](X1,X2,X3) = 1 [U45](X1,X2) = 1 [U46](X) = 1 [U51](X1,X2,X3) = 0 [U52](X1,X2,X3) = 1 [U53](X1,X2,X3) = 1 [U54](X1,X2,X3) = 1 [U55](X1,X2) = 0 [U56](X) = 1 [U61](X1,X2) = 0 [U62](X1,X2) = 1 [U63](X) = 1 [U71](X1,X2,X3) = 1 [U72](X1,X2) = 1 [U73](X1,X2) = 0 [U74](X) = 1 [U81](X1,X2) = 1 [U82](X1,X2) = 0 [U83](X) = 1 [U91](X1,X2) = 1 [U92](X) = 1 [__](X1,X2) = 1 [active](X) = 2 [isList](X) = 1 [isNeList](X) = 0 [isNePal](X) = 1 [isPal](X) = 1 [isPalListKind](X) = 1 [isQid](X) = 1 [mark](X) = 2 [a] = 2 [e] = 2 [i] = 2 [nil] = 2 [o] = 0 [tt] = 0 [u] = 1 [ACTIVE](X) = 2.X [MARK](X) = 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U12(X1,X2)) -> MARK(X1) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = X2 + 2 [U12](X1,X2) = X1 + X2 + 1 [U13](X) = X [U21](X1,X2,X3) = 2.X1 + 2.X2 + X3 + 2 [U22](X1,X2,X3) = 2.X1 + 2.X2 + X3 + 2 [U23](X1,X2,X3) = 2.X1 + 2.X2 + X3 + 2 [U24](X1,X2,X3) = 2.X1 + 2.X2 + X3 + 2 [U25](X1,X2) = 2.X1 + X2 [U26](X) = X [U31](X1,X2) = 2.X1 [U32](X1,X2) = 2.X1 [U33](X) = X [U41](X1,X2,X3) = 2.X1 + 2.X2 + X3 + 2 [U42](X1,X2,X3) = 2.X1 + 2.X2 + X3 + 2 [U43](X1,X2,X3) = 2.X1 + 2.X2 + X3 + 1 [U44](X1,X2,X3) = X1 + 2.X2 + X3 + 2 [U45](X1,X2) = X1 + X2 + 1 [U46](X) = X [U51](X1,X2,X3) = 2.X1 + 2.X2 + X3 + 2 [U52](X1,X2,X3) = 2.X1 + 2.X2 + X3 + 2 [U53](X1,X2,X3) = 2.X1 + 2.X2 + X3 + 1 [U54](X1,X2,X3) = 2.X1 + X2 + X3 + 1 [U55](X1,X2) = X1 + X2 + 1 [U56](X) = X [U61](X1,X2) = 2.X1 + 2.X2 [U62](X1,X2) = X1 + 2.X2 + 1 [U63](X) = X [U71](X1,X2,X3) = 2.X1 + X2 + 2.X3 + 2 [U72](X1,X2) = 2.X1 + 2.X2 + 2 [U73](X1,X2) = X1 + 2 [U74](X) = 2.X [U81](X1,X2) = 2.X1 + 2.X2 [U82](X1,X2) = X1 + 2.X2 + 1 [U83](X) = X [U91](X1,X2) = X1 [U92](X) = X [__](X1,X2) = 2.X1 + X2 + 2 [active](X) = X [isList](X) = X + 2 [isNeList](X) = X + 2 [isNePal](X) = 2.X + 2 [isPal](X) = 2.X + 2 [isPalListKind](X) = 1 [isQid](X) = 2 [mark](X) = X [a] = 0 [e] = 2 [i] = 2 [nil] = 2 [o] = 2 [tt] = 1 [u] = 2 [ACTIVE](X) = 2.X [MARK](X) = 2.X Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U13(X)) -> ACTIVE(U13(mark(X))) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = 1 [U12](X1,X2) = 0 [U13](X) = 0 [U21](X1,X2,X3) = 1 [U22](X1,X2,X3) = 1 [U23](X1,X2,X3) = 0 [U24](X1,X2,X3) = 1 [U25](X1,X2) = 1 [U26](X) = 1 [U31](X1,X2) = 1 [U32](X1,X2) = 0 [U33](X) = 0 [U41](X1,X2,X3) = 1 [U42](X1,X2,X3) = 1 [U43](X1,X2,X3) = 1 [U44](X1,X2,X3) = 1 [U45](X1,X2) = 1 [U46](X) = 0 [U51](X1,X2,X3) = 0 [U52](X1,X2,X3) = 1 [U53](X1,X2,X3) = 0 [U54](X1,X2,X3) = 1 [U55](X1,X2) = 1 [U56](X) = 1 [U61](X1,X2) = 1 [U62](X1,X2) = 1 [U63](X) = 1 [U71](X1,X2,X3) = 1 [U72](X1,X2) = 1 [U73](X1,X2) = 1 [U74](X) = 1 [U81](X1,X2) = 1 [U82](X1,X2) = 1 [U83](X) = 1 [U91](X1,X2) = 1 [U92](X) = 1 [__](X1,X2) = 1 [active](X) = 1 [isList](X) = 1 [isNeList](X) = 1 [isNePal](X) = 0 [isPal](X) = 1 [isPalListKind](X) = 1 [isQid](X) = 1 [mark](X) = 1 [a] = 2 [e] = 1 [i] = 0 [nil] = 2 [o] = 2 [tt] = 0 [u] = 1 [ACTIVE](X) = 2.X [MARK](X) = 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U13(X)) -> MARK(X) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = 2.X1 + 2.X2 [U12](X1,X2) = X1 + 2.X2 + 1 [U13](X) = X + 1 [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U22](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U23](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U24](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U25](X1,X2) = X1 + 2.X2 + 2 [U26](X) = X + 1 [U31](X1,X2) = X1 + 2.X2 [U32](X1,X2) = X1 + 2.X2 [U33](X) = 2.X [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U43](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U44](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U45](X1,X2) = X1 + 2.X2 + 2 [U46](X) = X + 2 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U52](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U53](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U54](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U55](X1,X2) = X1 + 2.X2 + 1 [U56](X) = X [U61](X1,X2) = X1 + 2.X2 + 1 [U62](X1,X2) = X1 + 2.X2 + 1 [U63](X) = X + 2 [U71](X1,X2,X3) = 2.X1 + X2 + 2.X3 + 2 [U72](X1,X2) = 2.X1 + 2.X2 + 2 [U73](X1,X2) = X1 + 2 [U74](X) = X + 2 [U81](X1,X2) = 2.X1 + 2.X2 [U82](X1,X2) = 2.X1 + 2.X2 [U83](X) = X [U91](X1,X2) = X1 [U92](X) = X [__](X1,X2) = 2.X1 + X2 + 2 [active](X) = X [isList](X) = 2.X + 2 [isNeList](X) = 2.X + 1 [isNePal](X) = 2.X + 2 [isPal](X) = 2.X + 2 [isPalListKind](X) = 1 [isQid](X) = X [mark](X) = X [a] = 2 [e] = 2 [i] = 2 [nil] = 2 [o] = 2 [tt] = 1 [u] = 2 [ACTIVE](X) = 2.X + 2 [MARK](X) = 2.X + 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U21(X1,X2,X3)) -> ACTIVE(U21(mark(X1),X2,X3)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = 0 [U12](X1,X2) = 2 [U13](X) = 1 [U21](X1,X2,X3) = 0 [U22](X1,X2,X3) = 0 [U23](X1,X2,X3) = 1 [U24](X1,X2,X3) = 1 [U25](X1,X2) = 1 [U26](X) = 1 [U31](X1,X2) = 1 [U32](X1,X2) = 1 [U33](X) = 1 [U41](X1,X2,X3) = 1 [U42](X1,X2,X3) = 1 [U43](X1,X2,X3) = 1 [U44](X1,X2,X3) = 1 [U45](X1,X2) = 1 [U46](X) = 1 [U51](X1,X2,X3) = 0 [U52](X1,X2,X3) = 1 [U53](X1,X2,X3) = 1 [U54](X1,X2,X3) = 1 [U55](X1,X2) = 1 [U56](X) = 1 [U61](X1,X2) = 1 [U62](X1,X2) = 1 [U63](X) = 1 [U71](X1,X2,X3) = 1 [U72](X1,X2) = 0 [U73](X1,X2) = 1 [U74](X) = 1 [U81](X1,X2) = 1 [U82](X1,X2) = 1 [U83](X) = 1 [U91](X1,X2) = 1 [U92](X) = 0 [__](X1,X2) = 0 [active](X) = 0 [isList](X) = 1 [isNeList](X) = 1 [isNePal](X) = 1 [isPal](X) = 1 [isPalListKind](X) = 1 [isQid](X) = 1 [mark](X) = 0 [a] = 0 [e] = 1 [i] = 2 [nil] = 0 [o] = 2 [tt] = 0 [u] = 2 [ACTIVE](X) = 2.X [MARK](X) = 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U21(X1,X2,X3)) -> MARK(X1) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = X1 + 2.X2 [U12](X1,X2) = 2.X2 + 2 [U13](X) = 2 [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U22](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U23](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U24](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U25](X1,X2) = X1 + 2.X2 + 2 [U26](X) = X + 2 [U31](X1,X2) = X1 + 2.X2 [U32](X1,X2) = X1 + 2.X2 [U33](X) = X [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 1 [U43](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 1 [U44](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 [U45](X1,X2) = X1 + 2.X2 + 2 [U46](X) = X + 2 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U52](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U53](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U54](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U55](X1,X2) = X1 + 2.X2 + 2 [U56](X) = X + 2 [U61](X1,X2) = X1 + 2.X2 [U62](X1,X2) = X1 + 2.X2 [U63](X) = X [U71](X1,X2,X3) = 2.X1 + 2.X3 + 2 [U72](X1,X2) = 2.X1 + 2.X2 + 1 [U73](X1,X2) = X1 + 2 [U74](X) = X + 2 [U81](X1,X2) = X1 + 2.X2 [U82](X1,X2) = X1 + 2.X2 [U83](X) = X [U91](X1,X2) = X1 [U92](X) = X [__](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 [isPalListKind](X) = 2 [isQid](X) = 2 [mark](X) = X [a] = 0 [e] = 2 [i] = 2 [nil] = 0 [o] = 2 [tt] = 2 [u] = 1 [ACTIVE](X) = 2.X + 2 [MARK](X) = 2.X + 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U22(X1,X2,X3)) -> ACTIVE(U22(mark(X1),X2,X3)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = 2 [U12](X1,X2) = 0 [U13](X) = 0 [U21](X1,X2,X3) = 0 [U22](X1,X2,X3) = 1 [U23](X1,X2,X3) = 0 [U24](X1,X2,X3) = 0 [U25](X1,X2) = 2 [U26](X) = 1 [U31](X1,X2) = 2 [U32](X1,X2) = 1 [U33](X) = 2 [U41](X1,X2,X3) = 2 [U42](X1,X2,X3) = 2 [U43](X1,X2,X3) = 2 [U44](X1,X2,X3) = 0 [U45](X1,X2) = 2 [U46](X) = 0 [U51](X1,X2,X3) = 2 [U52](X1,X2,X3) = 0 [U53](X1,X2,X3) = 0 [U54](X1,X2,X3) = 0 [U55](X1,X2) = 1 [U56](X) = 1 [U61](X1,X2) = 0 [U62](X1,X2) = 1 [U63](X) = 1 [U71](X1,X2,X3) = 2 [U72](X1,X2) = 1 [U73](X1,X2) = 1 [U74](X) = 2 [U81](X1,X2) = 2 [U82](X1,X2) = 2 [U83](X) = 2 [U91](X1,X2) = 2 [U92](X) = 0 [__](X1,X2) = 2 [active](X) = 2 [isList](X) = 2 [isNeList](X) = 2 [isNePal](X) = 2 [isPal](X) = 2 [isPalListKind](X) = 2 [isQid](X) = 1 [mark](X) = 2 [a] = 1 [e] = 2 [i] = 2 [nil] = 2 [o] = 2 [tt] = 0 [u] = 2 [ACTIVE](X) = X [MARK](X) = 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U22(X1,X2,X3)) -> MARK(X1) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = X1 + 2.X2 [U12](X1,X2) = 2.X2 + 2 [U13](X) = 2 [U21](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U22](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U23](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U24](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U25](X1,X2) = X1 + 2.X2 + 2 [U26](X) = X [U31](X1,X2) = X1 + 2.X2 [U32](X1,X2) = X1 + 2.X2 [U33](X) = X [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U43](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 1 [U44](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U45](X1,X2) = X1 + 2.X2 + 2 [U46](X) = X + 2 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U52](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 1 [U53](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U54](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U55](X1,X2) = X1 + 2.X2 + 2 [U56](X) = X + 2 [U61](X1,X2) = X1 + X2 [U62](X1,X2) = X1 + X2 [U63](X) = X [U71](X1,X2,X3) = 2.X1 + X2 + 2.X3 + 2 [U72](X1,X2) = 2.X1 + 2.X2 + 2 [U73](X1,X2) = 2.X1 + 1 [U74](X) = 2.X + 1 [U81](X1,X2) = X1 + X2 [U82](X1,X2) = X1 + X2 [U83](X) = X [U91](X1,X2) = X1 [U92](X) = X [__](X1,X2) = 2.X1 + X2 + 2 [active](X) = X [isList](X) = 2.X + 2 [isNeList](X) = 2.X + 2 [isNePal](X) = X + 2 [isPal](X) = X + 2 [isPalListKind](X) = 2 [isQid](X) = X + 2 [mark](X) = X [a] = 0 [e] = 0 [i] = 0 [nil] = 0 [o] = 2 [tt] = 2 [u] = 2 [ACTIVE](X) = 2.X + 2 [MARK](X) = 2.X + 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U23(X1,X2,X3)) -> ACTIVE(U23(mark(X1),X2,X3)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = 2.X1 [U12](X1,X2) = 0 [U13](X) = 0 [U21](X1,X2,X3) = 2.X1 + X2 + X3 + 2 [U22](X1,X2,X3) = X2 + X3 + 2 [U23](X1,X2,X3) = 2.X1 + X2 + X3 + 2 [U24](X1,X2,X3) = 2.X1 + X2 + X3 + 2 [U25](X1,X2) = X1 + X2 + 2 [U26](X) = X + 2 [U31](X1,X2) = 2.X1 + 2.X2 [U32](X1,X2) = 2.X1 + 2.X2 [U33](X) = 2.X [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U43](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U44](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U45](X1,X2) = X1 + 2.X2 + 2 [U46](X) = X + 2 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U52](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 [U53](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 [U54](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 [U55](X1,X2) = X1 + 2.X2 [U56](X) = 2.X [U61](X1,X2) = 2.X1 + 2.X2 + 2 [U62](X1,X2) = 2.X1 + 2 [U63](X) = 2.X + 2 [U71](X1,X2,X3) = 2.X1 + 2.X3 + 2 [U72](X1,X2) = 2.X1 + 2.X2 + 2 [U73](X1,X2) = X1 [U74](X) = 2.X [U81](X1,X2) = 2.X1 + 2.X2 + 2 [U82](X1,X2) = 2.X1 + 2.X2 + 2 [U83](X) = X [U91](X1,X2) = 2.X1 [U92](X) = X [__](X1,X2) = 2.X1 + X2 + 2 [active](X) = X [isList](X) = X [isNeList](X) = 2.X [isNePal](X) = 2.X + 2 [isPal](X) = 2.X + 2 [isPalListKind](X) = 0 [isQid](X) = 0 [mark](X) = X [a] = 2 [e] = 2 [i] = 0 [nil] = 2 [o] = 0 [tt] = 0 [u] = 0 [ACTIVE](X) = 2 [MARK](X) = 2.X + 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U23(X1,X2,X3)) -> MARK(X1) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = X2 + 2 [U12](X1,X2) = X1 [U13](X) = 2 [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U22](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U23](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U24](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 [U25](X1,X2) = X1 + 2.X2 + 2 [U26](X) = X + 2 [U31](X1,X2) = X1 + X2 [U32](X1,X2) = X1 + X2 [U33](X) = X [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 [U42](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U43](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 [U44](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U45](X1,X2) = X1 + 2.X2 + 1 [U46](X) = X + 1 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U52](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U53](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U54](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U55](X1,X2) = X1 + 2.X2 + 2 [U56](X) = X + 2 [U61](X1,X2) = X1 + 2.X2 [U62](X1,X2) = X1 + 2.X2 [U63](X) = X [U71](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U72](X1,X2) = X1 + 2.X2 + 2 [U73](X1,X2) = X1 + 2 [U74](X) = X + 2 [U81](X1,X2) = X1 + 2.X2 [U82](X1,X2) = X1 + 2.X2 [U83](X) = X [U91](X1,X2) = X1 [U92](X) = X [__](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 [isPalListKind](X) = 2 [isQid](X) = 2 [mark](X) = X [a] = 0 [e] = 2 [i] = 2 [nil] = 0 [o] = 0 [tt] = 2 [u] = 2 [ACTIVE](X) = 2.X + 1 [MARK](X) = 2.X + 1 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U24(X1,X2,X3)) -> ACTIVE(U24(mark(X1),X2,X3)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = 2.X1 [U12](X1,X2) = 0 [U13](X) = 0 [U21](X1,X2,X3) = 2.X2 + 2.X3 + 2 [U22](X1,X2,X3) = 2.X2 + 2.X3 + 2 [U23](X1,X2,X3) = 2.X2 + 2.X3 + 2 [U24](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U25](X1,X2) = X1 + 2.X2 + 2 [U26](X) = X + 1 [U31](X1,X2) = 2.X1 + 2.X2 + 2 [U32](X1,X2) = 2.X1 + 2.X2 + 2 [U33](X) = 2.X [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U43](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U44](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U45](X1,X2) = X1 + 2.X2 + 2 [U46](X) = X [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U52](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U53](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U54](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U55](X1,X2) = X1 + 2.X2 [U56](X) = X [U61](X1,X2) = 2.X1 + 2.X2 + 2 [U62](X1,X2) = 2.X1 + 2 [U63](X) = 2.X [U71](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U72](X1,X2) = 2.X1 + 2.X2 + 2 [U73](X1,X2) = X1 [U74](X) = 2.X [U81](X1,X2) = 2.X1 + 2.X2 + 2 [U82](X1,X2) = 2.X1 + 2.X2 + 2 [U83](X) = X [U91](X1,X2) = 2.X1 [U92](X) = 2.X [__](X1,X2) = X1 + X2 + 2 [active](X) = X [isList](X) = 2.X [isNeList](X) = 2.X + 2 [isNePal](X) = 2.X + 2 [isPal](X) = 2.X + 2 [isPalListKind](X) = 0 [isQid](X) = 1 [mark](X) = X [a] = 2 [e] = 2 [i] = 0 [nil] = 2 [o] = 2 [tt] = 0 [u] = 0 [ACTIVE](X) = 2 [MARK](X) = 2.X + 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U24(X1,X2,X3)) -> MARK(X1) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = X1 [U12](X1,X2) = 2 [U13](X) = 2 [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U22](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U23](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U24](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U25](X1,X2) = X1 + 2.X2 + 2 [U26](X) = X + 2 [U31](X1,X2) = X1 + 2.X2 [U32](X1,X2) = X1 + 2.X2 [U33](X) = X [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U43](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U44](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 [U45](X1,X2) = X1 + 2.X2 + 2 [U46](X) = X + 2 [U51](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U52](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 [U53](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 1 [U54](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 1 [U55](X1,X2) = X1 + 2.X2 + 1 [U56](X) = X + 1 [U61](X1,X2) = X1 [U62](X1,X2) = X1 [U63](X) = X [U71](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U72](X1,X2) = 2.X1 + 2.X2 + 2 [U73](X1,X2) = X1 + 2 [U74](X) = 2.X [U81](X1,X2) = X1 + 2.X2 [U82](X1,X2) = X1 + 2.X2 [U83](X) = X [U91](X1,X2) = X1 [U92](X) = X [__](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 [isPalListKind](X) = 2 [isQid](X) = 2 [mark](X) = X [a] = 2 [e] = 0 [i] = 2 [nil] = 2 [o] = 0 [tt] = 2 [u] = 2 [ACTIVE](X) = 2.X + 2 [MARK](X) = 2.X + 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U25(X1,X2)) -> ACTIVE(U25(mark(X1),X2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = 2 [U12](X1,X2) = 1 [U13](X) = 2 [U21](X1,X2,X3) = 2 [U22](X1,X2,X3) = 2 [U23](X1,X2,X3) = 1 [U24](X1,X2,X3) = 1 [U25](X1,X2) = 0 [U26](X) = 1 [U31](X1,X2) = 1 [U32](X1,X2) = 1 [U33](X) = 1 [U41](X1,X2,X3) = 1 [U42](X1,X2,X3) = 1 [U43](X1,X2,X3) = 1 [U44](X1,X2,X3) = 0 [U45](X1,X2) = 0 [U46](X) = 0 [U51](X1,X2,X3) = 1 [U52](X1,X2,X3) = 0 [U53](X1,X2,X3) = 1 [U54](X1,X2,X3) = 0 [U55](X1,X2) = 1 [U56](X) = 1 [U61](X1,X2) = 1 [U62](X1,X2) = 1 [U63](X) = 1 [U71](X1,X2,X3) = 1 [U72](X1,X2) = 1 [U73](X1,X2) = 1 [U74](X) = 0 [U81](X1,X2) = 1 [U82](X1,X2) = 1 [U83](X) = 1 [U91](X1,X2) = 1 [U92](X) = 1 [__](X1,X2) = 0 [active](X) = 2 [isList](X) = 1 [isNeList](X) = 0 [isNePal](X) = 0 [isPal](X) = 0 [isPalListKind](X) = 1 [isQid](X) = 1 [mark](X) = 2 [a] = 2 [e] = 2 [i] = 0 [nil] = 0 [o] = 2 [tt] = 0 [u] = 0 [ACTIVE](X) = 2.X [MARK](X) = 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U25(X1,X2)) -> MARK(X1) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = X1 + 2.X2 [U12](X1,X2) = 2.X2 + 2 [U13](X) = 2 [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U22](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U23](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U24](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U25](X1,X2) = X1 + 2.X2 + 2 [U26](X) = X + 2 [U31](X1,X2) = X1 + 2.X2 [U32](X1,X2) = X1 + 2.X2 [U33](X) = X [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U43](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U44](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U45](X1,X2) = X1 + 2.X2 + 2 [U46](X) = X + 2 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U52](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U53](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U54](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U55](X1,X2) = X1 + 2.X2 + 2 [U56](X) = X + 2 [U61](X1,X2) = X1 + 2.X2 [U62](X1,X2) = X1 + 2.X2 [U63](X) = X [U71](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U72](X1,X2) = X1 + 2.X2 + 2 [U73](X1,X2) = X1 + 2 [U74](X) = X + 2 [U81](X1,X2) = X1 + 2.X2 [U82](X1,X2) = X1 + 2.X2 [U83](X) = X [U91](X1,X2) = X1 [U92](X) = X [__](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 [isPalListKind](X) = 2 [isQid](X) = 2.X + 2 [mark](X) = X [a] = 1 [e] = 2 [i] = 1 [nil] = 2 [o] = 2 [tt] = 2 [u] = 1 [ACTIVE](X) = 2.X + 2 [MARK](X) = 2.X + 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U26(X)) -> ACTIVE(U26(mark(X))) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = X2 [U12](X1,X2) = X2 [U13](X) = 0 [U21](X1,X2,X3) = X1 + 2.X2 + X3 + 1 [U22](X1,X2,X3) = 2.X2 + X3 + 1 [U23](X1,X2,X3) = X1 + 2.X2 + X3 + 1 [U24](X1,X2,X3) = 2.X2 + X3 + 1 [U25](X1,X2) = 2.X1 + X2 + 1 [U26](X) = X + 1 [U31](X1,X2) = 2.X1 + 2 [U32](X1,X2) = 2.X1 + 2 [U33](X) = 2.X + 1 [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U43](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U44](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U45](X1,X2) = 2.X1 + 2.X2 + 2 [U46](X) = X [U51](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U52](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U53](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U54](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U55](X1,X2) = X1 + 2.X2 [U56](X) = 2.X [U61](X1,X2) = X1 + 2 [U62](X1,X2) = 2.X1 + 2 [U63](X) = 2.X + 2 [U71](X1,X2,X3) = 2.X1 + 2 [U72](X1,X2) = X1 + 2 [U73](X1,X2) = X1 [U74](X) = X [U81](X1,X2) = 2.X1 + 2 [U82](X1,X2) = 2.X1 + 2 [U83](X) = X [U91](X1,X2) = 2.X1 [U92](X) = 2.X [__](X1,X2) = 2.X1 + X2 + 1 [active](X) = X [isList](X) = X [isNeList](X) = 2.X + 2 [isNePal](X) = 2 [isPal](X) = 2 [isPalListKind](X) = 0 [isQid](X) = 0 [mark](X) = X [a] = 0 [e] = 2 [i] = 2 [nil] = 0 [o] = 0 [tt] = 0 [u] = 1 [ACTIVE](X) = 2 [MARK](X) = 2.X + 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U26(X)) -> MARK(X) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = X1 + 2.X2 [U12](X1,X2) = 2.X2 + 2 [U13](X) = 2 [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U22](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U23](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U24](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U25](X1,X2) = X1 + 2.X2 + 2 [U26](X) = X + 2 [U31](X1,X2) = X1 [U32](X1,X2) = X1 [U33](X) = X [U41](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U43](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U44](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 [U45](X1,X2) = X1 + 2.X2 + 2 [U46](X) = X + 2 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U52](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 1 [U53](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 1 [U54](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U55](X1,X2) = X1 + 2.X2 + 2 [U56](X) = X + 2 [U61](X1,X2) = X1 + X2 [U62](X1,X2) = X1 + X2 [U63](X) = X [U71](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U72](X1,X2) = X1 + 2.X2 + 2 [U73](X1,X2) = X1 + 1 [U74](X) = X + 1 [U81](X1,X2) = X1 + 2.X2 [U82](X1,X2) = X1 + 2.X2 [U83](X) = X [U91](X1,X2) = X1 [U92](X) = X [__](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 [isPalListKind](X) = 2 [isQid](X) = 2 [mark](X) = X [a] = 1 [e] = 1 [i] = 0 [nil] = 2 [o] = 2 [tt] = 2 [u] = 2 [ACTIVE](X) = 2.X + 2 [MARK](X) = 2.X + 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U31(X1,X2)) -> ACTIVE(U31(mark(X1),X2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = 2 [U12](X1,X2) = 2 [U13](X) = 0 [U21](X1,X2,X3) = 0 [U22](X1,X2,X3) = 2 [U23](X1,X2,X3) = 2 [U24](X1,X2,X3) = 1 [U25](X1,X2) = 1 [U26](X) = 2 [U31](X1,X2) = 0 [U32](X1,X2) = 1 [U33](X) = 0 [U41](X1,X2,X3) = 1 [U42](X1,X2,X3) = 1 [U43](X1,X2,X3) = 1 [U44](X1,X2,X3) = 0 [U45](X1,X2) = 1 [U46](X) = 1 [U51](X1,X2,X3) = 1 [U52](X1,X2,X3) = 1 [U53](X1,X2,X3) = 1 [U54](X1,X2,X3) = 1 [U55](X1,X2) = 1 [U56](X) = 0 [U61](X1,X2) = 0 [U62](X1,X2) = 1 [U63](X) = 1 [U71](X1,X2,X3) = 1 [U72](X1,X2) = 0 [U73](X1,X2) = 1 [U74](X) = 1 [U81](X1,X2) = 0 [U82](X1,X2) = 0 [U83](X) = 1 [U91](X1,X2) = 1 [U92](X) = 1 [__](X1,X2) = 1 [active](X) = 2 [isList](X) = 1 [isNeList](X) = 1 [isNePal](X) = 1 [isPal](X) = 1 [isPalListKind](X) = 1 [isQid](X) = 0 [mark](X) = 2 [a] = 1 [e] = 0 [i] = 2 [nil] = 0 [o] = 2 [tt] = 0 [u] = 0 [ACTIVE](X) = 2.X [MARK](X) = 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U31(X1,X2)) -> MARK(X1) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = X2 + 1 [U12](X1,X2) = X1 + X2 [U13](X) = 1 [U21](X1,X2,X3) = 2.X1 + 2.X2 + X3 [U22](X1,X2,X3) = 2.X1 + 2.X2 + X3 [U23](X1,X2,X3) = 2.X1 + X3 [U24](X1,X2,X3) = X3 + 2 [U25](X1,X2) = X2 + 2 [U26](X) = X [U31](X1,X2) = X1 + 2.X2 + 1 [U32](X1,X2) = X1 + 2.X2 + 1 [U33](X) = X [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U43](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U44](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U45](X1,X2) = 2.X1 + 2.X2 + 2 [U46](X) = X + 2 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U52](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U53](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U54](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U55](X1,X2) = X1 + 2.X2 + 2 [U56](X) = X + 2 [U61](X1,X2) = 2.X1 + 2.X2 [U62](X1,X2) = X1 + 2.X2 + 1 [U63](X) = X [U71](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U72](X1,X2) = 2.X1 + 2.X2 + 2 [U73](X1,X2) = X1 + 2 [U74](X) = 2.X + 1 [U81](X1,X2) = X1 + 2.X2 + 1 [U82](X1,X2) = X1 + 2.X2 + 1 [U83](X) = X [U91](X1,X2) = X1 [U92](X) = X [__](X1,X2) = 2.X1 + X2 + 2 [active](X) = X [isList](X) = X + 1 [isNeList](X) = 2.X + 2 [isNePal](X) = 2.X + 2 [isPal](X) = 2.X + 2 [isPalListKind](X) = 1 [isQid](X) = 2.X + 2 [mark](X) = X [a] = 2 [e] = 0 [i] = 1 [nil] = 2 [o] = 0 [tt] = 1 [u] = 1 [ACTIVE](X) = 2.X + 1 [MARK](X) = 2.X + 1 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U32(X1,X2)) -> ACTIVE(U32(mark(X1),X2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = 2.X2 [U12](X1,X2) = 2.X2 [U13](X) = 0 [U21](X1,X2,X3) = X1 + 2.X2 + X3 + 2 [U22](X1,X2,X3) = X1 + 2.X2 + X3 + 2 [U23](X1,X2,X3) = X1 + X2 + X3 + 2 [U24](X1,X2,X3) = X2 + X3 + 2 [U25](X1,X2) = X2 [U26](X) = 0 [U31](X1,X2) = X2 + 2 [U32](X1,X2) = X1 + 2 [U33](X) = 2.X + 2 [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U43](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U44](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U45](X1,X2) = X1 + 2.X2 + 2 [U46](X) = X [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U52](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U53](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U54](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U55](X1,X2) = X1 + 2.X2 [U56](X) = X [U61](X1,X2) = 2.X1 [U62](X1,X2) = X1 [U63](X) = X [U71](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U72](X1,X2) = X1 + 2.X2 + 2 [U73](X1,X2) = X1 [U74](X) = 2.X [U81](X1,X2) = 2.X1 + 2.X2 + 2 [U82](X1,X2) = 2.X1 + 2.X2 + 2 [U83](X) = X + 2 [U91](X1,X2) = X1 [U92](X) = 2.X [__](X1,X2) = 2.X1 + X2 + 2 [active](X) = X [isList](X) = 2.X [isNeList](X) = 2.X + 2 [isNePal](X) = 2.X [isPal](X) = 2.X + 2 [isPalListKind](X) = 0 [isQid](X) = 0 [mark](X) = X [a] = 2 [e] = 2 [i] = 0 [nil] = 2 [o] = 1 [tt] = 0 [u] = 0 [ACTIVE](X) = X + 2 [MARK](X) = 2.X + 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U32(X1,X2)) -> MARK(X1) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = 2 [U12](X1,X2) = 2 [U13](X) = 2 [U21](X1,X2,X3) = X1 + 2.X2 + X3 + 2 [U22](X1,X2,X3) = X1 + 2.X2 + X3 + 2 [U23](X1,X2,X3) = 2.X2 + 2 [U24](X1,X2,X3) = X1 + 1 [U25](X1,X2) = 2 [U26](X) = 1 [U31](X1,X2) = 2.X1 + X2 [U32](X1,X2) = X1 + X2 + 1 [U33](X) = 2.X [U41](X1,X2,X3) = 2.X1 + 2.X2 + X3 + 2 [U42](X1,X2,X3) = X1 + 2.X2 + X3 + 2 [U43](X1,X2,X3) = 2.X1 + 2.X2 + X3 + 1 [U44](X1,X2,X3) = X1 + 2.X2 + X3 + 2 [U45](X1,X2) = X1 + X2 + 1 [U46](X) = X [U51](X1,X2,X3) = 2.X1 + 2.X2 + X3 + 2 [U52](X1,X2,X3) = 2.X1 + 2.X2 + X3 + 2 [U53](X1,X2,X3) = 2.X1 + 2.X2 + X3 + 2 [U54](X1,X2,X3) = 2.X1 + 2.X2 + X3 + 2 [U55](X1,X2) = 2.X1 + X2 [U56](X) = X [U61](X1,X2) = X1 + X2 [U62](X1,X2) = X1 [U63](X) = X [U71](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U72](X1,X2) = 2.X1 + 2.X2 + 2 [U73](X1,X2) = 2.X1 + 2 [U74](X) = 2.X + 2 [U81](X1,X2) = X1 + X2 [U82](X1,X2) = X1 + X2 [U83](X) = X [U91](X1,X2) = X1 [U92](X) = X [__](X1,X2) = 2.X1 + X2 + 2 [active](X) = X [isList](X) = X + 2 [isNeList](X) = X + 2 [isNePal](X) = X + 1 [isPal](X) = X + 1 [isPalListKind](X) = 1 [isQid](X) = 1 [mark](X) = X [a] = 0 [e] = 1 [i] = 0 [nil] = 2 [o] = 0 [tt] = 1 [u] = 2 [ACTIVE](X) = 2.X + 2 [MARK](X) = 2.X + 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U33(X)) -> ACTIVE(U33(mark(X))) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = 1 [U12](X1,X2) = 0 [U13](X) = 0 [U21](X1,X2,X3) = 2 [U22](X1,X2,X3) = 0 [U23](X1,X2,X3) = 0 [U24](X1,X2,X3) = 2 [U25](X1,X2) = 2 [U26](X) = 1 [U31](X1,X2) = 1 [U32](X1,X2) = 2 [U33](X) = 0 [U41](X1,X2,X3) = 1 [U42](X1,X2,X3) = 1 [U43](X1,X2,X3) = 1 [U44](X1,X2,X3) = 0 [U45](X1,X2) = 1 [U46](X) = 1 [U51](X1,X2,X3) = 1 [U52](X1,X2,X3) = 1 [U53](X1,X2,X3) = 1 [U54](X1,X2,X3) = 1 [U55](X1,X2) = 1 [U56](X) = 1 [U61](X1,X2) = 1 [U62](X1,X2) = 1 [U63](X) = 1 [U71](X1,X2,X3) = 1 [U72](X1,X2) = 0 [U73](X1,X2) = 1 [U74](X) = 1 [U81](X1,X2) = 1 [U82](X1,X2) = 1 [U83](X) = 1 [U91](X1,X2) = 1 [U92](X) = 1 [__](X1,X2) = 1 [active](X) = 2 [isList](X) = 1 [isNeList](X) = 1 [isNePal](X) = 0 [isPal](X) = 0 [isPalListKind](X) = 1 [isQid](X) = 1 [mark](X) = 2 [a] = 1 [e] = 0 [i] = 0 [nil] = 0 [o] = 0 [tt] = 2 [u] = 0 [ACTIVE](X) = 2.X [MARK](X) = 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U33(X)) -> MARK(X) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = 2.X2 + 2 [U12](X1,X2) = X2 + 2 [U13](X) = 2 [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U22](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U23](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U24](X1,X2,X3) = X1 + X2 + 2.X3 [U25](X1,X2) = 2.X2 + 2 [U26](X) = 2 [U31](X1,X2) = X1 + 2.X2 [U32](X1,X2) = 2.X2 + 2 [U33](X) = X + 1 [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U43](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U44](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U45](X1,X2) = X1 + 2.X2 + 2 [U46](X) = X + 2 [U51](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U52](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 [U53](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U54](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U55](X1,X2) = X1 + 2.X2 + 2 [U56](X) = X + 2 [U61](X1,X2) = X1 + X2 [U62](X1,X2) = X1 + X2 [U63](X) = X + 1 [U71](X1,X2,X3) = 2.X1 + X2 + 2.X3 + 2 [U72](X1,X2) = 2.X1 + 2.X2 + 2 [U73](X1,X2) = 2.X1 + 2 [U74](X) = X + 2 [U81](X1,X2) = X1 + X2 [U82](X1,X2) = X1 + X2 [U83](X) = X [U91](X1,X2) = X1 [U92](X) = X [__](X1,X2) = 2.X1 + X2 + 2 [active](X) = X [isList](X) = 2.X + 2 [isNeList](X) = 2.X + 2 [isNePal](X) = X + 2 [isPal](X) = X + 2 [isPalListKind](X) = 2 [isQid](X) = X + 1 [mark](X) = X [a] = 2 [e] = 2 [i] = 2 [nil] = 2 [o] = 2 [tt] = 2 [u] = 2 [ACTIVE](X) = 2.X + 2 [MARK](X) = 2.X + 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U41(X1,X2,X3)) -> ACTIVE(U41(mark(X1),X2,X3)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = 2.X2 [U12](X1,X2) = 2.X2 [U13](X) = X [U21](X1,X2,X3) = 2.X2 + 2.X3 + 2 [U22](X1,X2,X3) = 2.X2 + 2.X3 + 2 [U23](X1,X2,X3) = 2.X2 + 2.X3 + 2 [U24](X1,X2,X3) = 2.X2 + 2.X3 + 1 [U25](X1,X2) = X1 + 2.X2 + 1 [U26](X) = 1 [U31](X1,X2) = X1 + 2.X2 [U32](X1,X2) = 2.X2 [U33](X) = 2.X [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U43](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U44](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U45](X1,X2) = X1 + 2.X2 + 2 [U46](X) = X + 2 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U52](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U53](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U54](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U55](X1,X2) = X1 + 2.X2 + 2 [U56](X) = X + 2 [U61](X1,X2) = 2.X1 + 2.X2 + 1 [U62](X1,X2) = 2.X1 + 2.X2 + 1 [U63](X) = 2.X + 1 [U71](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U72](X1,X2) = X1 + 2.X2 + 2 [U73](X1,X2) = X1 [U74](X) = 2.X [U81](X1,X2) = X1 + 2.X2 + 2 [U82](X1,X2) = 2.X1 + 2.X2 + 2 [U83](X) = X + 1 [U91](X1,X2) = 2.X1 [U92](X) = X [__](X1,X2) = 2.X1 + X2 + 2 [active](X) = X [isList](X) = 2.X [isNeList](X) = 2.X [isNePal](X) = 2.X + 1 [isPal](X) = 2.X + 2 [isPalListKind](X) = 0 [isQid](X) = X [mark](X) = X [a] = 1 [e] = 0 [i] = 2 [nil] = 2 [o] = 2 [tt] = 0 [u] = 0 [ACTIVE](X) = X + 2 [MARK](X) = 2.X + 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U41(X1,X2,X3)) -> MARK(X1) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = X1 + X2 [U12](X1,X2) = X2 + 2 [U13](X) = 2 [U21](X1,X2,X3) = 2.X1 + 2.X2 + X3 [U22](X1,X2,X3) = 2.X1 + 2.X2 [U23](X1,X2,X3) = X1 + 2.X2 + 2 [U24](X1,X2,X3) = X1 + 2.X2 + 2 [U25](X1,X2) = 2.X1 [U26](X) = 2 [U31](X1,X2) = X1 + 2.X2 [U32](X1,X2) = X1 [U33](X) = X [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U43](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U44](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U45](X1,X2) = 2.X1 + 2.X2 + 2 [U46](X) = X + 2 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 [U52](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 [U53](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U54](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 [U55](X1,X2) = X1 + 2.X2 + 2 [U56](X) = 2.X [U61](X1,X2) = X1 [U62](X1,X2) = X1 [U63](X) = X [U71](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U72](X1,X2) = 2.X1 + 2.X2 + 2 [U73](X1,X2) = 2.X1 + 2 [U74](X) = 2.X [U81](X1,X2) = X1 + X2 [U82](X1,X2) = X1 + X2 [U83](X) = X [U91](X1,X2) = X1 [U92](X) = X [__](X1,X2) = 2.X1 + X2 + 2 [active](X) = X [isList](X) = X + 2 [isNeList](X) = 2.X + 2 [isNePal](X) = X + 2 [isPal](X) = X + 2 [isPalListKind](X) = 2 [isQid](X) = 2 [mark](X) = X [a] = 0 [e] = 2 [i] = 0 [nil] = 0 [o] = 2 [tt] = 2 [u] = 2 [ACTIVE](X) = 2.X + 2 [MARK](X) = 2.X + 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U42(X1,X2,X3)) -> ACTIVE(U42(mark(X1),X2,X3)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = 1 [U12](X1,X2) = 2 [U13](X) = 2 [U21](X1,X2,X3) = 2 [U22](X1,X2,X3) = 2 [U23](X1,X2,X3) = 2 [U24](X1,X2,X3) = 2 [U25](X1,X2) = 2 [U26](X) = 2 [U31](X1,X2) = 2 [U32](X1,X2) = 2 [U33](X) = 1 [U41](X1,X2,X3) = 2 [U42](X1,X2,X3) = 0 [U43](X1,X2,X3) = 1 [U44](X1,X2,X3) = 0 [U45](X1,X2) = 1 [U46](X) = 1 [U51](X1,X2,X3) = 1 [U52](X1,X2,X3) = 1 [U53](X1,X2,X3) = 1 [U54](X1,X2,X3) = 1 [U55](X1,X2) = 1 [U56](X) = 0 [U61](X1,X2) = 1 [U62](X1,X2) = 1 [U63](X) = 1 [U71](X1,X2,X3) = 1 [U72](X1,X2) = 1 [U73](X1,X2) = 1 [U74](X) = 1 [U81](X1,X2) = 1 [U82](X1,X2) = 1 [U83](X) = 1 [U91](X1,X2) = 1 [U92](X) = 1 [__](X1,X2) = 0 [active](X) = 2 [isList](X) = 0 [isNeList](X) = 1 [isNePal](X) = 1 [isPal](X) = 1 [isPalListKind](X) = 1 [isQid](X) = 1 [mark](X) = 2 [a] = 1 [e] = 2 [i] = 2 [nil] = 0 [o] = 1 [tt] = 0 [u] = 2 [ACTIVE](X) = 2.X [MARK](X) = 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U42(X1,X2,X3)) -> MARK(X1) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = 2.X2 + 2 [U12](X1,X2) = 2.X2 + 2 [U13](X) = 2 [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U22](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U23](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U24](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U25](X1,X2) = X1 + 2.X2 + 2 [U26](X) = 2 [U31](X1,X2) = 2.X2 + 2 [U32](X1,X2) = 2 [U33](X) = 2 [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U43](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 1 [U44](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U45](X1,X2) = X1 + 2.X2 + 2 [U46](X) = X + 2 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U52](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U53](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U54](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 [U55](X1,X2) = X1 + 2.X2 + 2 [U56](X) = X + 2 [U61](X1,X2) = X1 + X2 [U62](X1,X2) = X1 + X2 [U63](X) = X [U71](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U72](X1,X2) = 2.X1 + 2.X2 + 2 [U73](X1,X2) = 2.X1 + 2 [U74](X) = X [U81](X1,X2) = X1 + X2 [U82](X1,X2) = X1 + X2 [U83](X) = X [U91](X1,X2) = X1 [U92](X) = X [__](X1,X2) = 2.X1 + X2 + 2 [active](X) = X [isList](X) = 2.X + 2 [isNeList](X) = 2.X + 2 [isNePal](X) = X + 2 [isPal](X) = X + 2 [isPalListKind](X) = 2 [isQid](X) = 2 [mark](X) = X [a] = 0 [e] = 2 [i] = 0 [nil] = 1 [o] = 0 [tt] = 2 [u] = 2 [ACTIVE](X) = 2.X + 2 [MARK](X) = 2.X + 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U43(X1,X2,X3)) -> ACTIVE(U43(mark(X1),X2,X3)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = 2.X2 + 2 [U12](X1,X2) = X1 + 2.X2 + 2 [U13](X) = X + 2 [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U22](X1,X2,X3) = 2.X2 + 2.X3 + 2 [U23](X1,X2,X3) = 2.X2 + 2.X3 + 2 [U24](X1,X2,X3) = X2 + 2 [U25](X1,X2) = 2 [U26](X) = 2 [U31](X1,X2) = 0 [U32](X1,X2) = 0 [U33](X) = 2.X [U41](X1,X2,X3) = 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = 2.X2 + 2.X3 + 2 [U43](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U44](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U45](X1,X2) = X1 + 2.X2 [U46](X) = X [U51](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U52](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U53](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U54](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U55](X1,X2) = X1 + 2.X2 + 2 [U56](X) = X [U61](X1,X2) = 2.X1 + X2 [U62](X1,X2) = 2.X1 + X2 [U63](X) = X [U71](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U72](X1,X2) = 2.X1 + 2.X2 + 2 [U73](X1,X2) = X1 [U74](X) = 2.X [U81](X1,X2) = 2.X1 + 2.X2 + 2 [U82](X1,X2) = X1 + 2.X2 + 2 [U83](X) = 2.X + 2 [U91](X1,X2) = 2.X1 [U92](X) = 2.X [__](X1,X2) = 2.X1 + X2 + 2 [active](X) = X [isList](X) = 2.X + 2 [isNeList](X) = 2.X [isNePal](X) = X [isPal](X) = 2.X + 2 [isPalListKind](X) = 0 [isQid](X) = 0 [mark](X) = X [a] = 0 [e] = 2 [i] = 0 [nil] = 2 [o] = 0 [tt] = 0 [u] = 0 [ACTIVE](X) = 2 [MARK](X) = 2.X + 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U43(X1,X2,X3)) -> MARK(X1) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = 2.X2 + 2 [U12](X1,X2) = 2.X2 + 2 [U13](X) = 2 [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U22](X1,X2,X3) = 2.X2 + 2.X3 + 2 [U23](X1,X2,X3) = 2.X2 + 2.X3 + 2 [U24](X1,X2,X3) = 2.X3 + 2 [U25](X1,X2) = 2.X2 + 2 [U26](X) = 2 [U31](X1,X2) = X1 + 2.X2 [U32](X1,X2) = X1 [U33](X) = 2 [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U43](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U44](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U45](X1,X2) = X1 + 2.X2 + 2 [U46](X) = X + 2 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U52](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U53](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U54](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U55](X1,X2) = X1 + 2.X2 + 2 [U56](X) = X + 2 [U61](X1,X2) = X1 + 2.X2 [U62](X1,X2) = X1 + 2.X2 [U63](X) = X [U71](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 [U72](X1,X2) = X1 + 2.X2 + 2 [U73](X1,X2) = X1 + 2 [U74](X) = X + 2 [U81](X1,X2) = X1 + 2.X2 [U82](X1,X2) = X1 + 2.X2 [U83](X) = X [U91](X1,X2) = X1 [U92](X) = X [__](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 [isPalListKind](X) = 2 [isQid](X) = 2.X + 2 [mark](X) = X [a] = 0 [e] = 1 [i] = 0 [nil] = 1 [o] = 2 [tt] = 2 [u] = 2 [ACTIVE](X) = 2.X + 2 [MARK](X) = 2.X + 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U44(X1,X2,X3)) -> ACTIVE(U44(mark(X1),X2,X3)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = 2 [U12](X1,X2) = 2 [U13](X) = 2 [U21](X1,X2,X3) = 1 [U22](X1,X2,X3) = 1 [U23](X1,X2,X3) = 2 [U24](X1,X2,X3) = 2 [U25](X1,X2) = 2 [U26](X) = 2 [U31](X1,X2) = 1 [U32](X1,X2) = 2 [U33](X) = 2 [U41](X1,X2,X3) = 2 [U42](X1,X2,X3) = 2 [U43](X1,X2,X3) = 0 [U44](X1,X2,X3) = 1 [U45](X1,X2) = 2 [U46](X) = 2 [U51](X1,X2,X3) = 1 [U52](X1,X2,X3) = 1 [U53](X1,X2,X3) = 2 [U54](X1,X2,X3) = 2 [U55](X1,X2) = 1 [U56](X) = 0 [U61](X1,X2) = 1 [U62](X1,X2) = 2 [U63](X) = 2 [U71](X1,X2,X3) = 2 [U72](X1,X2) = 2 [U73](X1,X2) = 2 [U74](X) = 2 [U81](X1,X2) = 2 [U82](X1,X2) = 2 [U83](X) = 2 [U91](X1,X2) = 2 [U92](X) = 2 [__](X1,X2) = 1 [active](X) = 2 [isList](X) = 0 [isNeList](X) = 2 [isNePal](X) = 2 [isPal](X) = 0 [isPalListKind](X) = 2 [isQid](X) = 2 [mark](X) = 2 [a] = 0 [e] = 0 [i] = 0 [nil] = 2 [o] = 2 [tt] = 0 [u] = 1 [ACTIVE](X) = X [MARK](X) = 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U44(X1,X2,X3)) -> MARK(X1) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = 2.X2 + 2 [U12](X1,X2) = X2 + 2 [U13](X) = 2 [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U22](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U23](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U24](X1,X2,X3) = 2.X2 + 2.X3 + 2 [U25](X1,X2) = X1 + 2.X2 [U26](X) = 2 [U31](X1,X2) = X1 + 2.X2 [U32](X1,X2) = 2.X2 + 2 [U33](X) = 2 [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U43](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U44](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U45](X1,X2) = X1 + 2.X2 + 2 [U46](X) = X + 2 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U52](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U53](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U54](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U55](X1,X2) = X1 + 2.X2 + 2 [U56](X) = X [U61](X1,X2) = X1 + 2.X2 [U62](X1,X2) = X1 + 2.X2 [U63](X) = X + 1 [U71](X1,X2,X3) = 2.X1 + 2.X3 + 2 [U72](X1,X2) = X1 + 2.X2 + 2 [U73](X1,X2) = X1 + 2 [U74](X) = X + 2 [U81](X1,X2) = X1 + 2.X2 [U82](X1,X2) = X1 + 2.X2 [U83](X) = X [U91](X1,X2) = X1 [U92](X) = X [__](X1,X2) = 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 [isPalListKind](X) = 2 [isQid](X) = 2.X [mark](X) = X [a] = 2 [e] = 2 [i] = 2 [nil] = 2 [o] = 2 [tt] = 2 [u] = 1 [ACTIVE](X) = 2.X + 2 [MARK](X) = 2.X + 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U45(X1,X2)) -> ACTIVE(U45(mark(X1),X2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = 2 [U12](X1,X2) = 0 [U13](X) = 2 [U21](X1,X2,X3) = 2 [U22](X1,X2,X3) = 2 [U23](X1,X2,X3) = 2 [U24](X1,X2,X3) = 0 [U25](X1,X2) = 2 [U26](X) = 0 [U31](X1,X2) = 0 [U32](X1,X2) = 2 [U33](X) = 2 [U41](X1,X2,X3) = 2 [U42](X1,X2,X3) = 0 [U43](X1,X2,X3) = 2 [U44](X1,X2,X3) = 2 [U45](X1,X2) = 1 [U46](X) = 0 [U51](X1,X2,X3) = 1 [U52](X1,X2,X3) = 2 [U53](X1,X2,X3) = 2 [U54](X1,X2,X3) = 2 [U55](X1,X2) = 2 [U56](X) = 2 [U61](X1,X2) = 2 [U62](X1,X2) = 2 [U63](X) = 2 [U71](X1,X2,X3) = 0 [U72](X1,X2) = 1 [U73](X1,X2) = 2 [U74](X) = 2 [U81](X1,X2) = 2 [U82](X1,X2) = 2 [U83](X) = 2 [U91](X1,X2) = 2 [U92](X) = 0 [__](X1,X2) = 2 [active](X) = 2 [isList](X) = 2 [isNeList](X) = 0 [isNePal](X) = 0 [isPal](X) = 1 [isPalListKind](X) = 2 [isQid](X) = 2 [mark](X) = 2 [a] = 2 [e] = 2 [i] = 2 [nil] = 2 [o] = 1 [tt] = 0 [u] = 2 [ACTIVE](X) = X [MARK](X) = 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U45(X1,X2)) -> MARK(X1) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = 2.X2 + 2 [U12](X1,X2) = X1 + 2.X2 [U13](X) = 2 [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U22](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U23](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U24](X1,X2,X3) = X1 + 2.X3 + 2 [U25](X1,X2) = 2.X2 + 2 [U26](X) = 2 [U31](X1,X2) = 2.X2 + 2 [U32](X1,X2) = X1 + 2.X2 [U33](X) = X [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U43](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U44](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U45](X1,X2) = X1 + 2.X2 + 2 [U46](X) = X + 1 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 1 [U52](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U53](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U54](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U55](X1,X2) = X1 + 2.X2 + 2 [U56](X) = X + 2 [U61](X1,X2) = X1 + 2.X2 [U62](X1,X2) = X1 + 2.X2 [U63](X) = X [U71](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U72](X1,X2) = X1 + 2.X2 + 2 [U73](X1,X2) = X1 + 2 [U74](X) = 2.X [U81](X1,X2) = X1 + 2.X2 [U82](X1,X2) = X1 + 2.X2 [U83](X) = X [U91](X1,X2) = X1 [U92](X) = X [__](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 [isPalListKind](X) = 2 [isQid](X) = 2.X + 2 [mark](X) = X [a] = 2 [e] = 2 [i] = 2 [nil] = 2 [o] = 1 [tt] = 2 [u] = 0 [ACTIVE](X) = 2.X + 2 [MARK](X) = 2.X + 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U46(X)) -> ACTIVE(U46(mark(X))) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = 2 [U12](X1,X2) = 1 [U13](X) = 2 [U21](X1,X2,X3) = 2 [U22](X1,X2,X3) = 0 [U23](X1,X2,X3) = 0 [U24](X1,X2,X3) = 2 [U25](X1,X2) = 2 [U26](X) = 2 [U31](X1,X2) = 2 [U32](X1,X2) = 2 [U33](X) = 2 [U41](X1,X2,X3) = 2 [U42](X1,X2,X3) = 2 [U43](X1,X2,X3) = 2 [U44](X1,X2,X3) = 2 [U45](X1,X2) = 0 [U46](X) = 0 [U51](X1,X2,X3) = 1 [U52](X1,X2,X3) = 1 [U53](X1,X2,X3) = 1 [U54](X1,X2,X3) = 0 [U55](X1,X2) = 1 [U56](X) = 1 [U61](X1,X2) = 0 [U62](X1,X2) = 1 [U63](X) = 0 [U71](X1,X2,X3) = 1 [U72](X1,X2) = 1 [U73](X1,X2) = 1 [U74](X) = 1 [U81](X1,X2) = 1 [U82](X1,X2) = 1 [U83](X) = 1 [U91](X1,X2) = 1 [U92](X) = 1 [__](X1,X2) = 1 [active](X) = 1 [isList](X) = 1 [isNeList](X) = 1 [isNePal](X) = 1 [isPal](X) = 0 [isPalListKind](X) = 1 [isQid](X) = 0 [mark](X) = 1 [a] = 2 [e] = 0 [i] = 0 [nil] = 2 [o] = 2 [tt] = 0 [u] = 2 [ACTIVE](X) = 2.X [MARK](X) = 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U46(X)) -> MARK(X) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = X1 + 2.X2 [U12](X1,X2) = 2.X2 + 2 [U13](X) = 2 [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U22](X1,X2,X3) = 2.X1 + 2.X2 + X3 + 2 [U23](X1,X2,X3) = 2.X1 + 2.X2 + X3 + 2 [U24](X1,X2,X3) = X1 + 2.X2 + X3 + 2 [U25](X1,X2) = X1 + 1 [U26](X) = 2 [U31](X1,X2) = X1 + 2.X2 [U32](X1,X2) = 2.X2 + 2 [U33](X) = 2.X [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U43](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 1 [U44](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 1 [U45](X1,X2) = X1 + 2.X2 + 2 [U46](X) = X + 2 [U51](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U52](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 [U53](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U54](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U55](X1,X2) = X1 + 2.X2 + 2 [U56](X) = X + 2 [U61](X1,X2) = X1 + 2.X2 [U62](X1,X2) = X1 + 2.X2 [U63](X) = X + 1 [U71](X1,X2,X3) = 2.X1 + 2.X3 + 2 [U72](X1,X2) = 2.X1 + 2.X2 + 2 [U73](X1,X2) = X1 + 2 [U74](X) = X + 2 [U81](X1,X2) = X1 + 2.X2 [U82](X1,X2) = X1 + 2.X2 [U83](X) = X [U91](X1,X2) = X1 [U92](X) = X [__](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 [isPalListKind](X) = 2 [isQid](X) = X + 1 [mark](X) = X [a] = 2 [e] = 1 [i] = 2 [nil] = 2 [o] = 2 [tt] = 2 [u] = 2 [ACTIVE](X) = 2.X [MARK](X) = 2.X Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U51(X1,X2,X3)) -> ACTIVE(U51(mark(X1),X2,X3)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = 2 [U12](X1,X2) = 2 [U13](X) = 2 [U21](X1,X2,X3) = 0 [U22](X1,X2,X3) = 0 [U23](X1,X2,X3) = 0 [U24](X1,X2,X3) = 2 [U25](X1,X2) = 0 [U26](X) = 2 [U31](X1,X2) = 0 [U32](X1,X2) = 2 [U33](X) = 2 [U41](X1,X2,X3) = 2 [U42](X1,X2,X3) = 2 [U43](X1,X2,X3) = 2 [U44](X1,X2,X3) = 2 [U45](X1,X2) = 2 [U46](X) = 1 [U51](X1,X2,X3) = 0 [U52](X1,X2,X3) = 2 [U53](X1,X2,X3) = 1 [U54](X1,X2,X3) = 1 [U55](X1,X2) = 0 [U56](X) = 2 [U61](X1,X2) = 2 [U62](X1,X2) = 1 [U63](X) = 0 [U71](X1,X2,X3) = 2 [U72](X1,X2) = 2 [U73](X1,X2) = 2 [U74](X) = 0 [U81](X1,X2) = 1 [U82](X1,X2) = 0 [U83](X) = 0 [U91](X1,X2) = 2 [U92](X) = 2 [__](X1,X2) = 2 [active](X) = 2 [isList](X) = 2 [isNeList](X) = 2 [isNePal](X) = 2 [isPal](X) = 2 [isPalListKind](X) = 2 [isQid](X) = 0 [mark](X) = 2 [a] = 0 [e] = 0 [i] = 1 [nil] = 0 [o] = 0 [tt] = 2 [u] = 0 [ACTIVE](X) = X [MARK](X) = 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U51(X1,X2,X3)) -> MARK(X1) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = 2.X2 + 2 [U12](X1,X2) = 2.X2 + 2 [U13](X) = X [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U22](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U23](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U24](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U25](X1,X2) = X1 + 2.X2 + 2 [U26](X) = X + 2 [U31](X1,X2) = X1 + 2.X2 [U32](X1,X2) = 2.X2 [U33](X) = 2.X [U41](X1,X2,X3) = 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = 2.X2 + 2.X3 + 2 [U43](X1,X2,X3) = X3 + 2 [U44](X1,X2,X3) = X3 + 2 [U45](X1,X2) = X2 + 2 [U46](X) = 2 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U52](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U53](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U54](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U55](X1,X2) = X1 + 2.X2 + 2 [U56](X) = X [U61](X1,X2) = X1 + 2.X2 [U62](X1,X2) = X1 + 2.X2 [U63](X) = 2.X + 1 [U71](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U72](X1,X2) = 2.X1 + 2.X2 + 2 [U73](X1,X2) = X1 + 2 [U74](X) = X + 2 [U81](X1,X2) = X1 + 2.X2 [U82](X1,X2) = X1 + 2.X2 [U83](X) = X [U91](X1,X2) = X1 [U92](X) = X [__](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 [isPalListKind](X) = 2 [isQid](X) = X [mark](X) = X [a] = 2 [e] = 2 [i] = 2 [nil] = 2 [o] = 2 [tt] = 2 [u] = 2 [ACTIVE](X) = 2.X + 2 [MARK](X) = 2.X + 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U52(X1,X2,X3)) -> ACTIVE(U52(mark(X1),X2,X3)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = 2.X1 + X2 [U12](X1,X2) = X2 [U13](X) = 0 [U21](X1,X2,X3) = X1 + 2.X3 + 2 [U22](X1,X2,X3) = 2.X3 + 2 [U23](X1,X2,X3) = X1 + 2.X3 + 2 [U24](X1,X2,X3) = 2.X3 + 2 [U25](X1,X2) = 2.X2 + 2 [U26](X) = 2 [U31](X1,X2) = 2.X2 [U32](X1,X2) = 0 [U33](X) = 0 [U41](X1,X2,X3) = 2.X3 + 2 [U42](X1,X2,X3) = 2.X1 + 2.X3 + 2 [U43](X1,X2,X3) = 2.X3 + 2 [U44](X1,X2,X3) = 2.X3 + 2 [U45](X1,X2) = 2.X2 + 2 [U46](X) = X + 2 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U52](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U53](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U54](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U55](X1,X2) = X1 + 2.X2 + 2 [U56](X) = X + 2 [U61](X1,X2) = 2.X1 + 2.X2 + 2 [U62](X1,X2) = 2.X1 + 2.X2 + 2 [U63](X) = X + 2 [U71](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U72](X1,X2) = X1 + 2.X2 + 2 [U73](X1,X2) = X1 [U74](X) = 2.X [U81](X1,X2) = X1 + 2.X2 + 2 [U82](X1,X2) = 2.X1 + 2.X2 + 2 [U83](X) = X [U91](X1,X2) = 2.X1 [U92](X) = X [__](X1,X2) = 2.X1 + X2 + 2 [active](X) = X [isList](X) = 2.X [isNeList](X) = 2.X [isNePal](X) = 2.X + 2 [isPal](X) = 2.X + 2 [isPalListKind](X) = 0 [isQid](X) = 2.X [mark](X) = X [a] = 2 [e] = 2 [i] = 2 [nil] = 2 [o] = 2 [tt] = 0 [u] = 2 [ACTIVE](X) = 2 [MARK](X) = 2.X + 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U52(X1,X2,X3)) -> MARK(X1) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = X1 + 2.X2 [U12](X1,X2) = 2.X2 + 2 [U13](X) = 2 [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U22](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U23](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U24](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 1 [U25](X1,X2) = 2.X2 + 2 [U26](X) = 2 [U31](X1,X2) = X1 + 2.X2 [U32](X1,X2) = 2.X2 + 2 [U33](X) = 2 [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U43](X1,X2,X3) = 2.X2 + 2.X3 + 2 [U44](X1,X2,X3) = X1 + 2.X2 + 2.X3 [U45](X1,X2) = 2.X2 + 2 [U46](X) = 2 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U52](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U53](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U54](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U55](X1,X2) = X1 + 2.X2 + 2 [U56](X) = X + 2 [U61](X1,X2) = X1 + X2 [U62](X1,X2) = X1 + X2 [U63](X) = X [U71](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U72](X1,X2) = 2.X1 + 2.X2 + 2 [U73](X1,X2) = 2.X1 + 2 [U74](X) = 2.X + 2 [U81](X1,X2) = X1 + X2 [U82](X1,X2) = X1 + X2 [U83](X) = X [U91](X1,X2) = X1 [U92](X) = X [__](X1,X2) = 2.X1 + X2 + 2 [active](X) = X [isList](X) = 2.X + 2 [isNeList](X) = 2.X + 2 [isNePal](X) = X + 2 [isPal](X) = X + 2 [isPalListKind](X) = 2 [isQid](X) = 2 [mark](X) = X [a] = 0 [e] = 0 [i] = 0 [nil] = 1 [o] = 0 [tt] = 2 [u] = 1 [ACTIVE](X) = 2.X + 2 [MARK](X) = 2.X + 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U53(X1,X2,X3)) -> ACTIVE(U53(mark(X1),X2,X3)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = X2 [U12](X1,X2) = X1 [U13](X) = 0 [U21](X1,X2,X3) = 2.X2 + X3 + 2 [U22](X1,X2,X3) = 2.X2 + X3 + 2 [U23](X1,X2,X3) = 2.X2 + X3 + 2 [U24](X1,X2,X3) = X1 + 2.X2 + X3 + 2 [U25](X1,X2) = 2.X1 + 1 [U26](X) = 1 [U31](X1,X2) = X1 + 2.X2 [U32](X1,X2) = 2.X2 [U33](X) = 0 [U41](X1,X2,X3) = X2 + 2.X3 + 2 [U42](X1,X2,X3) = 2.X3 + 2 [U43](X1,X2,X3) = 2.X1 + X3 + 2 [U44](X1,X2,X3) = 2 [U45](X1,X2) = 2 [U46](X) = 2 [U51](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U52](X1,X2,X3) = 2.X2 + 2.X3 + 2 [U53](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U54](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U55](X1,X2) = X1 + 2.X2 + 2 [U56](X) = 2.X + 2 [U61](X1,X2) = 2.X1 + 2 [U62](X1,X2) = 2.X1 + 2 [U63](X) = 2.X + 2 [U71](X1,X2,X3) = 2.X1 + 2 [U72](X1,X2) = 2.X1 + 2 [U73](X1,X2) = X1 [U74](X) = 2.X [U81](X1,X2) = X1 + 2 [U82](X1,X2) = 2.X1 + 2 [U83](X) = X [U91](X1,X2) = 2.X1 [U92](X) = X [__](X1,X2) = 2.X1 + X2 + 2 [active](X) = X [isList](X) = X [isNeList](X) = 2.X [isNePal](X) = 2 [isPal](X) = 2 [isPalListKind](X) = 0 [isQid](X) = 0 [mark](X) = X [a] = 0 [e] = 1 [i] = 0 [nil] = 0 [o] = 0 [tt] = 0 [u] = 1 [ACTIVE](X) = 2 [MARK](X) = 2.X + 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U53(X1,X2,X3)) -> MARK(X1) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = X1 [U12](X1,X2) = 2 [U13](X) = 2 [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U22](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U23](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U24](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U25](X1,X2) = X1 + 2.X2 + 2 [U26](X) = 2 [U31](X1,X2) = X2 + 2 [U32](X1,X2) = X2 + 2 [U33](X) = 2 [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 1 [U42](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U43](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U44](X1,X2,X3) = 2.X1 + 2.X3 [U45](X1,X2) = X2 + 2 [U46](X) = 2 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U52](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U53](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U54](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 [U55](X1,X2) = X1 + 2.X2 + 2 [U56](X) = X + 2 [U61](X1,X2) = X1 + 2.X2 [U62](X1,X2) = X1 + 2.X2 [U63](X) = X + 2 [U71](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U72](X1,X2) = 2.X1 + 2.X2 + 2 [U73](X1,X2) = X1 + 2 [U74](X) = 2.X [U81](X1,X2) = X1 + 2.X2 [U82](X1,X2) = X1 + 2.X2 [U83](X) = X [U91](X1,X2) = X1 [U92](X) = X [__](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 [isPalListKind](X) = 2 [isQid](X) = 2.X [mark](X) = X [a] = 1 [e] = 1 [i] = 1 [nil] = 2 [o] = 2 [tt] = 2 [u] = 2 [ACTIVE](X) = 2.X + 2 [MARK](X) = 2.X + 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U54(X1,X2,X3)) -> ACTIVE(U54(mark(X1),X2,X3)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = 2.X1 + X2 [U12](X1,X2) = X2 [U13](X) = 0 [U21](X1,X2,X3) = 2.X2 + X3 + 2 [U22](X1,X2,X3) = 2.X1 + X2 + X3 + 2 [U23](X1,X2,X3) = X2 + X3 + 2 [U24](X1,X2,X3) = 2.X1 + X2 + X3 [U25](X1,X2) = X1 [U26](X) = 0 [U31](X1,X2) = 2.X1 + X2 + 1 [U32](X1,X2) = 2.X1 + X2 + 1 [U33](X) = 1 [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = 2.X2 + 2.X3 + 1 [U43](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 1 [U44](X1,X2,X3) = 2.X2 + 2.X3 + 1 [U45](X1,X2) = 2.X1 + 2.X2 + 1 [U46](X) = 0 [U51](X1,X2,X3) = 2.X2 + 2.X3 + 2 [U52](X1,X2,X3) = 2.X2 + 2.X3 + 2 [U53](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U54](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U55](X1,X2) = X1 + 2.X2 [U56](X) = 2.X [U61](X1,X2) = 2.X1 + 2.X2 + 2 [U62](X1,X2) = 2.X1 + 2.X2 + 2 [U63](X) = X [U71](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U72](X1,X2) = 2.X1 + 2.X2 + 2 [U73](X1,X2) = X1 [U74](X) = 2.X [U81](X1,X2) = 2.X1 + 2.X2 + 2 [U82](X1,X2) = 2.X1 + 2.X2 + 2 [U83](X) = X [U91](X1,X2) = 2.X1 [U92](X) = 2.X [__](X1,X2) = 2.X1 + X2 + 2 [active](X) = X [isList](X) = X [isNeList](X) = 2.X + 2 [isNePal](X) = 2.X + 2 [isPal](X) = 2.X + 2 [isPalListKind](X) = 0 [isQid](X) = 2 [mark](X) = X [a] = 2 [e] = 0 [i] = 0 [nil] = 0 [o] = 0 [tt] = 0 [u] = 0 [ACTIVE](X) = X + 2 [MARK](X) = 2.X + 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U54(X1,X2,X3)) -> MARK(X1) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = 2.X2 + 2 [U12](X1,X2) = X2 + 2 [U13](X) = 2 [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U22](X1,X2,X3) = 2.X1 + 2.X3 + 2 [U23](X1,X2,X3) = 2.X1 + 2.X3 [U24](X1,X2,X3) = X1 + 2.X3 + 2 [U25](X1,X2) = 2.X2 + 2 [U26](X) = 2 [U31](X1,X2) = X1 + 2.X2 [U32](X1,X2) = X1 + 2.X2 [U33](X) = 2 [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U43](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U44](X1,X2,X3) = X1 + 2.X3 + 1 [U45](X1,X2) = 2.X2 + 2 [U46](X) = 2 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U52](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U53](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U54](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U55](X1,X2) = X1 + 2.X2 + 2 [U56](X) = X + 2 [U61](X1,X2) = X1 + 2.X2 [U62](X1,X2) = X1 + 2.X2 [U63](X) = X [U71](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U72](X1,X2) = 2.X1 + 2.X2 + 2 [U73](X1,X2) = X1 + 1 [U74](X) = X [U81](X1,X2) = X1 + 2.X2 [U82](X1,X2) = X1 + 2.X2 [U83](X) = X [U91](X1,X2) = X1 [U92](X) = X [__](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 [isPalListKind](X) = 2 [isQid](X) = 2.X + 2 [mark](X) = X [a] = 1 [e] = 0 [i] = 1 [nil] = 0 [o] = 0 [tt] = 2 [u] = 1 [ACTIVE](X) = 2.X + 2 [MARK](X) = 2.X + 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U55(X1,X2)) -> ACTIVE(U55(mark(X1),X2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = 2 [U12](X1,X2) = 2 [U13](X) = 2 [U21](X1,X2,X3) = 2 [U22](X1,X2,X3) = 1 [U23](X1,X2,X3) = 2 [U24](X1,X2,X3) = 1 [U25](X1,X2) = 2 [U26](X) = 2 [U31](X1,X2) = 0 [U32](X1,X2) = 2 [U33](X) = 2 [U41](X1,X2,X3) = 2 [U42](X1,X2,X3) = 1 [U43](X1,X2,X3) = 2 [U44](X1,X2,X3) = 2 [U45](X1,X2) = 2 [U46](X) = 2 [U51](X1,X2,X3) = 2 [U52](X1,X2,X3) = 0 [U53](X1,X2,X3) = 0 [U54](X1,X2,X3) = 0 [U55](X1,X2) = 0 [U56](X) = 1 [U61](X1,X2) = 0 [U62](X1,X2) = 1 [U63](X) = 0 [U71](X1,X2,X3) = 1 [U72](X1,X2) = 1 [U73](X1,X2) = 0 [U74](X) = 1 [U81](X1,X2) = 1 [U82](X1,X2) = 1 [U83](X) = 1 [U91](X1,X2) = 1 [U92](X) = 1 [__](X1,X2) = 1 [active](X) = 2 [isList](X) = 1 [isNeList](X) = 1 [isNePal](X) = 0 [isPal](X) = 1 [isPalListKind](X) = 1 [isQid](X) = 1 [mark](X) = 2 [a] = 2 [e] = 2 [i] = 2 [nil] = 2 [o] = 1 [tt] = 1 [u] = 1 [ACTIVE](X) = 2.X [MARK](X) = 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U55(X1,X2)) -> MARK(X1) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = X1 + 2.X2 [U12](X1,X2) = 2.X2 + 2 [U13](X) = 2 [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U22](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U23](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U24](X1,X2,X3) = 2.X1 + 2.X2 + 2 [U25](X1,X2) = X1 + 2 [U26](X) = 2 [U31](X1,X2) = 2 [U32](X1,X2) = 2 [U33](X) = 2 [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = 2.X1 + 2.X2 + 2 [U43](X1,X2,X3) = X1 + 2.X2 + 2 [U44](X1,X2,X3) = X1 + 2.X2 + 2 [U45](X1,X2) = 2 [U46](X) = 2 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U52](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U53](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U54](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U55](X1,X2) = X1 + 2.X2 + 2 [U56](X) = X + 2 [U61](X1,X2) = X1 + 2.X2 [U62](X1,X2) = X1 + 2.X2 [U63](X) = X [U71](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 [U72](X1,X2) = X1 + 2.X2 + 2 [U73](X1,X2) = X1 + 2 [U74](X) = X + 1 [U81](X1,X2) = X1 + 2.X2 [U82](X1,X2) = X1 + 2.X2 [U83](X) = X [U91](X1,X2) = X1 [U92](X) = X [__](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 [isPalListKind](X) = 2 [isQid](X) = 2.X + 2 [mark](X) = X [a] = 2 [e] = 1 [i] = 2 [nil] = 0 [o] = 0 [tt] = 2 [u] = 0 [ACTIVE](X) = 2.X + 2 [MARK](X) = 2.X + 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U56(X)) -> ACTIVE(U56(mark(X))) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = 0 [U12](X1,X2) = 2.X1 [U13](X) = 0 [U21](X1,X2,X3) = 0 [U22](X1,X2,X3) = 0 [U23](X1,X2,X3) = 0 [U24](X1,X2,X3) = 0 [U25](X1,X2) = 0 [U26](X) = 2.X [U31](X1,X2) = 2 [U32](X1,X2) = 2 [U33](X) = 2 [U41](X1,X2,X3) = 2.X3 + 2 [U42](X1,X2,X3) = 2.X3 + 2 [U43](X1,X2,X3) = 2.X3 + 2 [U44](X1,X2,X3) = 2.X3 + 2 [U45](X1,X2) = 2.X1 + 2.X2 + 2 [U46](X) = 2 [U51](X1,X2,X3) = X2 + 2.X3 + 2 [U52](X1,X2,X3) = X2 + 2.X3 + 2 [U53](X1,X2,X3) = X2 + 2.X3 + 2 [U54](X1,X2,X3) = 2.X1 + X2 + X3 + 2 [U55](X1,X2) = X2 + 2 [U56](X) = X + 2 [U61](X1,X2) = 2.X1 + 2.X2 + 2 [U62](X1,X2) = 2.X1 + 2 [U63](X) = X [U71](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U72](X1,X2) = 2.X1 + 2.X2 + 2 [U73](X1,X2) = X1 [U74](X) = 2.X [U81](X1,X2) = 2.X1 + 2.X2 + 2 [U82](X1,X2) = 2.X1 + 2.X2 + 2 [U83](X) = X [U91](X1,X2) = 2.X1 [U92](X) = 2.X [__](X1,X2) = X1 + X2 + 1 [active](X) = X [isList](X) = 0 [isNeList](X) = 2.X + 2 [isNePal](X) = 2.X + 2 [isPal](X) = 2.X + 2 [isPalListKind](X) = 0 [isQid](X) = 2 [mark](X) = X [a] = 2 [e] = 2 [i] = 2 [nil] = 2 [o] = 0 [tt] = 0 [u] = 2 [ACTIVE](X) = 2 [MARK](X) = 2.X + 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U56(X)) -> MARK(X) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = 2.X2 + 2 [U12](X1,X2) = X2 + 2 [U13](X) = 2 [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U22](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U23](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U24](X1,X2,X3) = X2 + 2.X3 + 2 [U25](X1,X2) = 2.X2 + 2 [U26](X) = X [U31](X1,X2) = 2.X2 + 2 [U32](X1,X2) = 2.X2 + 2 [U33](X) = 2 [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 [U42](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U43](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 [U44](X1,X2,X3) = 2.X1 + X2 + 2.X3 [U45](X1,X2) = 2.X2 + 2 [U46](X) = X [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U52](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 [U53](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 [U54](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U55](X1,X2) = X1 + 2.X2 + 2 [U56](X) = X + 2 [U61](X1,X2) = X1 + 2.X2 [U62](X1,X2) = X1 + 2.X2 [U63](X) = X [U71](X1,X2,X3) = 2.X1 + 2.X3 + 2 [U72](X1,X2) = X1 + 2.X2 + 2 [U73](X1,X2) = X1 + 2 [U74](X) = 2.X [U81](X1,X2) = X1 + 2.X2 [U82](X1,X2) = X1 + 2.X2 [U83](X) = X [U91](X1,X2) = X1 [U92](X) = X [__](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 [isPalListKind](X) = 2 [isQid](X) = 2 [mark](X) = X [a] = 0 [e] = 2 [i] = 1 [nil] = 0 [o] = 0 [tt] = 2 [u] = 0 [ACTIVE](X) = 2.X + 2 [MARK](X) = 2.X + 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U61(X1,X2)) -> ACTIVE(U61(mark(X1),X2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = X2 + 1 [U12](X1,X2) = X2 + 1 [U13](X) = 1 [U21](X1,X2,X3) = 2.X2 + X3 + 2 [U22](X1,X2,X3) = 2.X2 + X3 + 2 [U23](X1,X2,X3) = 2.X2 + X3 + 2 [U24](X1,X2,X3) = 2.X2 + X3 + 2 [U25](X1,X2) = 2.X1 [U26](X) = 0 [U31](X1,X2) = 2.X2 + 2 [U32](X1,X2) = 2.X2 + 2 [U33](X) = 2 [U41](X1,X2,X3) = 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = 2.X2 + X3 + 2 [U43](X1,X2,X3) = 2.X2 + X3 + 2 [U44](X1,X2,X3) = 2.X2 + 2 [U45](X1,X2) = 2.X1 [U46](X) = 0 [U51](X1,X2,X3) = 2.X2 + 2 [U52](X1,X2,X3) = 2.X2 + 2 [U53](X1,X2,X3) = 2.X2 + 2 [U54](X1,X2,X3) = 2.X2 + 2 [U55](X1,X2) = 2 [U56](X) = 2 [U61](X1,X2) = X1 + X2 + 2 [U62](X1,X2) = X1 + X2 + 2 [U63](X) = X [U71](X1,X2,X3) = X1 + 2.X3 + 2 [U72](X1,X2) = X1 + 2.X2 + 2 [U73](X1,X2) = X1 [U74](X) = 2.X [U81](X1,X2) = X1 + 2.X2 + 2 [U82](X1,X2) = X1 + 2.X2 + 2 [U83](X) = X [U91](X1,X2) = 2.X1 [U92](X) = X [__](X1,X2) = 2.X1 + X2 + 2 [active](X) = X [isList](X) = X + 1 [isNeList](X) = 2.X + 2 [isNePal](X) = 2.X + 2 [isPal](X) = 2.X + 2 [isPalListKind](X) = 0 [isQid](X) = 2 [mark](X) = X [a] = 2 [e] = 2 [i] = 2 [nil] = 2 [o] = 0 [tt] = 0 [u] = 2 [ACTIVE](X) = 0 [MARK](X) = 2.X Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U61(X1,X2)) -> MARK(X1) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = 2.X1 + 2.X2 [U12](X1,X2) = X1 + 2.X2 + 1 [U13](X) = 2 [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 [U22](X1,X2,X3) = 2.X2 + 2.X3 + 2 [U23](X1,X2,X3) = 2.X2 + 2.X3 + 2 [U24](X1,X2,X3) = 2.X2 + 2.X3 + 2 [U25](X1,X2) = X1 + 2.X2 [U26](X) = 1 [U31](X1,X2) = X2 + 2 [U32](X1,X2) = X2 + 2 [U33](X) = 2 [U41](X1,X2,X3) = 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 [U43](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 [U44](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 [U45](X1,X2) = 2.X2 + 1 [U46](X) = 1 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 [U52](X1,X2,X3) = 2.X1 + 2.X3 [U53](X1,X2,X3) = 2.X1 + 2.X3 [U54](X1,X2,X3) = 2.X1 + 2.X3 [U55](X1,X2) = 2.X2 + 2 [U56](X) = X [U61](X1,X2) = X1 + 2.X2 + 1 [U62](X1,X2) = 2.X1 + 2.X2 [U63](X) = 2.X + 2 [U71](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U72](X1,X2) = 2.X1 + 2.X2 + 2 [U73](X1,X2) = X1 + 2 [U74](X) = X + 2 [U81](X1,X2) = 2.X1 + 2.X2 [U82](X1,X2) = 2.X1 + 2.X2 [U83](X) = X [U91](X1,X2) = X1 [U92](X) = X [__](X1,X2) = 2.X1 + X2 [active](X) = X [isList](X) = 2.X + 2 [isNeList](X) = 2.X + 2 [isNePal](X) = 2.X + 2 [isPal](X) = 2.X + 2 [isPalListKind](X) = 1 [isQid](X) = X [mark](X) = X [a] = 2 [e] = 1 [i] = 2 [nil] = 2 [o] = 2 [tt] = 1 [u] = 2 [ACTIVE](X) = 2.X + 2 [MARK](X) = 2.X + 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U62(X1,X2)) -> ACTIVE(U62(mark(X1),X2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = X2 + 1 [U12](X1,X2) = 2.X1 + X2 + 1 [U13](X) = 1 [U21](X1,X2,X3) = X1 + 2.X2 + X3 + 2 [U22](X1,X2,X3) = 2.X2 + X3 + 2 [U23](X1,X2,X3) = X1 + 2.X2 + X3 + 2 [U24](X1,X2,X3) = 2.X2 + X3 + 2 [U25](X1,X2) = 2.X1 + X2 [U26](X) = 0 [U31](X1,X2) = 2.X2 + 2 [U32](X1,X2) = X2 + 2 [U33](X) = 2 [U41](X1,X2,X3) = 2.X2 + X3 + 2 [U42](X1,X2,X3) = 2.X2 + 2 [U43](X1,X2,X3) = X1 + 2.X2 + 2 [U44](X1,X2,X3) = 2.X2 + 2 [U45](X1,X2) = 2 [U46](X) = 0 [U51](X1,X2,X3) = 2.X2 + 2.X3 + 2 [U52](X1,X2,X3) = 2.X2 + X3 + 2 [U53](X1,X2,X3) = 2.X2 + X3 + 2 [U54](X1,X2,X3) = 2.X2 + 2 [U55](X1,X2) = 2 [U56](X) = 2 [U61](X1,X2) = 2.X1 + 2.X2 + 2 [U62](X1,X2) = 2.X1 + 2.X2 + 2 [U63](X) = X [U71](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U72](X1,X2) = 2.X1 + 2.X2 + 2 [U73](X1,X2) = X1 [U74](X) = X [U81](X1,X2) = 2.X1 + 2.X2 + 2 [U82](X1,X2) = 2.X1 + 2.X2 + 2 [U83](X) = X [U91](X1,X2) = 2.X1 [U92](X) = 2.X [__](X1,X2) = 2.X1 + X2 + 2 [active](X) = X [isList](X) = X + 1 [isNeList](X) = 2.X + 2 [isNePal](X) = 2.X + 2 [isPal](X) = 2.X + 2 [isPalListKind](X) = 0 [isQid](X) = 2.X + 2 [mark](X) = X [a] = 0 [e] = 0 [i] = 0 [nil] = 2 [o] = 2 [tt] = 0 [u] = 2 [ACTIVE](X) = 2 [MARK](X) = 2.X + 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U62(X1,X2)) -> MARK(X1) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = 2.X1 [U12](X1,X2) = 2.X1 [U13](X) = 0 [U21](X1,X2,X3) = 0 [U22](X1,X2,X3) = 0 [U23](X1,X2,X3) = 0 [U24](X1,X2,X3) = 0 [U25](X1,X2) = 0 [U26](X) = 2.X [U31](X1,X2) = X2 + 1 [U32](X1,X2) = X2 + 1 [U33](X) = 1 [U41](X1,X2,X3) = 2.X1 + 2.X2 + X3 + 2 [U42](X1,X2,X3) = 2.X1 + 2.X2 + X3 + 2 [U43](X1,X2,X3) = 2.X2 + X3 + 2 [U44](X1,X2,X3) = 2.X1 + 2.X2 + X3 + 2 [U45](X1,X2) = 2 [U46](X) = 2 [U51](X1,X2,X3) = 2.X2 + X3 + 2 [U52](X1,X2,X3) = 2.X2 + X3 + 2 [U53](X1,X2,X3) = 2.X2 + X3 + 2 [U54](X1,X2,X3) = 2.X2 + X3 + 2 [U55](X1,X2) = 2.X1 + X2 [U56](X) = 2.X [U61](X1,X2) = 2 [U62](X1,X2) = X1 + 2 [U63](X) = 2.X + 2 [U71](X1,X2,X3) = 2.X1 + 2 [U72](X1,X2) = 2.X1 + 2 [U73](X1,X2) = X1 [U74](X) = 2.X [U81](X1,X2) = 2.X1 + 2 [U82](X1,X2) = X1 + 2 [U83](X) = X [U91](X1,X2) = 2.X1 [U92](X) = 2.X [__](X1,X2) = 2.X1 + X2 + 2 [active](X) = X [isList](X) = 0 [isNeList](X) = X + 1 [isNePal](X) = 2 [isPal](X) = 2 [isPalListKind](X) = 0 [isQid](X) = 0 [mark](X) = X [a] = 2 [e] = 0 [i] = 0 [nil] = 2 [o] = 0 [tt] = 0 [u] = 2 [ACTIVE](X) = 2.X + 1 [MARK](X) = 2.X + 1 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U63(X)) -> ACTIVE(U63(mark(X))) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = 2.X2 + 2 [U12](X1,X2) = X2 [U13](X) = 0 [U21](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U22](X1,X2,X3) = 2.X3 + 2 [U23](X1,X2,X3) = 2.X3 + 2 [U24](X1,X2,X3) = X1 + 2.X3 + 2 [U25](X1,X2) = 2.X2 + 2 [U26](X) = X [U31](X1,X2) = 2.X1 + 2.X2 + 2 [U32](X1,X2) = X1 + 2.X2 + 2 [U33](X) = 2.X [U41](X1,X2,X3) = 2.X1 + X2 + 2.X3 + 2 [U42](X1,X2,X3) = X2 + 2.X3 + 2 [U43](X1,X2,X3) = 2.X1 + X2 + X3 + 2 [U44](X1,X2,X3) = X2 + X3 + 2 [U45](X1,X2) = X2 [U46](X) = 0 [U51](X1,X2,X3) = 2.X1 + 2.X2 + X3 + 2 [U52](X1,X2,X3) = X1 + 2.X2 + 1 [U53](X1,X2,X3) = 2.X1 + 2.X2 + 1 [U54](X1,X2,X3) = 2.X1 + 2.X2 [U55](X1,X2) = 0 [U56](X) = 0 [U61](X1,X2) = 2.X1 + 2.X2 + 1 [U62](X1,X2) = 2.X2 + 1 [U63](X) = X + 1 [U71](X1,X2,X3) = 2.X1 + X2 + 2.X3 + 2 [U72](X1,X2) = X1 + 2.X2 + 2 [U73](X1,X2) = X1 [U74](X) = X [U81](X1,X2) = 2.X1 + 2.X2 + 2 [U82](X1,X2) = 2.X1 + 2.X2 + 1 [U83](X) = X [U91](X1,X2) = 2.X1 [U92](X) = X [__](X1,X2) = X1 + X2 + 2 [active](X) = X [isList](X) = 2.X + 2 [isNeList](X) = 2.X + 2 [isNePal](X) = 2.X + 1 [isPal](X) = 2.X + 2 [isPalListKind](X) = 0 [isQid](X) = 0 [mark](X) = X [a] = 1 [e] = 0 [i] = 2 [nil] = 0 [o] = 1 [tt] = 0 [u] = 1 [ACTIVE](X) = X + 1 [MARK](X) = 2.X + 1 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U63(X)) -> MARK(X) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = 2.X2 + 2 [U12](X1,X2) = 2.X2 + 2 [U13](X) = 2 [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U22](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U23](X1,X2,X3) = 2.X2 + 2.X3 + 2 [U24](X1,X2,X3) = 2.X2 + 2.X3 + 2 [U25](X1,X2) = 2 [U26](X) = 2 [U31](X1,X2) = 2.X2 + 2 [U32](X1,X2) = 2.X2 + 2 [U33](X) = 2 [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = 2.X2 + 2.X3 + 2 [U43](X1,X2,X3) = 2.X2 + 2.X3 + 2 [U44](X1,X2,X3) = 2.X1 + X2 + 2.X3 + 2 [U45](X1,X2) = 2.X2 + 2 [U46](X) = 2 [U51](X1,X2,X3) = 2.X2 + 2.X3 + 2 [U52](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U53](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U54](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U55](X1,X2) = X1 + 2.X2 [U56](X) = 0 [U61](X1,X2) = 2.X2 + 2 [U62](X1,X2) = 2.X2 + 2 [U63](X) = X + 1 [U71](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U72](X1,X2) = 2.X1 + 2.X2 + 2 [U73](X1,X2) = X1 [U74](X) = X [U81](X1,X2) = X1 + 2.X2 + 2 [U82](X1,X2) = 2.X1 + 2.X2 + 2 [U83](X) = X [U91](X1,X2) = 2.X1 [U92](X) = 2.X [__](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 [isPalListKind](X) = 0 [isQid](X) = 2.X + 1 [mark](X) = X [a] = 0 [e] = 2 [i] = 0 [nil] = 2 [o] = 2 [tt] = 0 [u] = 2 [ACTIVE](X) = 2.X + 2 [MARK](X) = 2.X + 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U71(X1,X2,X3)) -> ACTIVE(U71(mark(X1),X2,X3)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = 2 [U12](X1,X2) = 1 [U13](X) = 2 [U21](X1,X2,X3) = 1 [U22](X1,X2,X3) = 1 [U23](X1,X2,X3) = 2 [U24](X1,X2,X3) = 2 [U25](X1,X2) = 2 [U26](X) = 2 [U31](X1,X2) = 2 [U32](X1,X2) = 0 [U33](X) = 1 [U41](X1,X2,X3) = 2 [U42](X1,X2,X3) = 2 [U43](X1,X2,X3) = 2 [U44](X1,X2,X3) = 2 [U45](X1,X2) = 2 [U46](X) = 1 [U51](X1,X2,X3) = 1 [U52](X1,X2,X3) = 1 [U53](X1,X2,X3) = 2 [U54](X1,X2,X3) = 2 [U55](X1,X2) = 1 [U56](X) = 0 [U61](X1,X2) = 2 [U62](X1,X2) = 2 [U63](X) = 2 [U71](X1,X2,X3) = 0 [U72](X1,X2) = 1 [U73](X1,X2) = 1 [U74](X) = 1 [U81](X1,X2) = 1 [U82](X1,X2) = 1 [U83](X) = 1 [U91](X1,X2) = 1 [U92](X) = 1 [__](X1,X2) = 0 [active](X) = 2 [isList](X) = 1 [isNeList](X) = 0 [isNePal](X) = 1 [isPal](X) = 0 [isPalListKind](X) = 1 [isQid](X) = 1 [mark](X) = 2 [a] = 0 [e] = 0 [i] = 2 [nil] = 0 [o] = 0 [tt] = 0 [u] = 0 [ACTIVE](X) = 2.X [MARK](X) = 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U71(X1,X2,X3)) -> MARK(X1) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = 2.X2 + 2 [U12](X1,X2) = 2.X2 + 2 [U13](X) = 2 [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U22](X1,X2,X3) = 2.X1 + 2.X2 + 2 [U23](X1,X2,X3) = 2.X1 + 2.X2 + 2 [U24](X1,X2,X3) = X1 + 2.X2 + 2 [U25](X1,X2) = 2 [U26](X) = 2 [U31](X1,X2) = 2.X2 + 2 [U32](X1,X2) = X1 + 2.X2 [U33](X) = 2 [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U43](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 [U44](X1,X2,X3) = 2.X2 + 2.X3 + 2 [U45](X1,X2) = X1 + 2.X2 [U46](X) = X [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U52](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U53](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U54](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 [U55](X1,X2) = X1 + 1 [U56](X) = 2 [U61](X1,X2) = X1 + 2.X2 [U62](X1,X2) = 2.X2 + 2 [U63](X) = X [U71](X1,X2,X3) = 2.X1 + 2.X3 + 2 [U72](X1,X2) = 2.X1 + 2.X2 + 2 [U73](X1,X2) = X1 + 2 [U74](X) = 2.X [U81](X1,X2) = X1 + 2.X2 [U82](X1,X2) = X1 + 2.X2 [U83](X) = X [U91](X1,X2) = X1 [U92](X) = X [__](X1,X2) = 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 [isPalListKind](X) = 2 [isQid](X) = X + 2 [mark](X) = X [a] = 2 [e] = 0 [i] = 2 [nil] = 2 [o] = 2 [tt] = 2 [u] = 2 [ACTIVE](X) = 2.X + 2 [MARK](X) = 2.X + 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U72(X1,X2)) -> ACTIVE(U72(mark(X1),X2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = 2 [U12](X1,X2) = 0 [U13](X) = 2 [U21](X1,X2,X3) = 1 [U22](X1,X2,X3) = 0 [U23](X1,X2,X3) = 1 [U24](X1,X2,X3) = 1 [U25](X1,X2) = 2 [U26](X) = 1 [U31](X1,X2) = 2 [U32](X1,X2) = 2 [U33](X) = 2 [U41](X1,X2,X3) = 2 [U42](X1,X2,X3) = 2 [U43](X1,X2,X3) = 2 [U44](X1,X2,X3) = 2 [U45](X1,X2) = 2 [U46](X) = 2 [U51](X1,X2,X3) = 0 [U52](X1,X2,X3) = 1 [U53](X1,X2,X3) = 0 [U54](X1,X2,X3) = 0 [U55](X1,X2) = 2 [U56](X) = 2 [U61](X1,X2) = 2 [U62](X1,X2) = 2 [U63](X) = 2 [U71](X1,X2,X3) = 2 [U72](X1,X2) = 0 [U73](X1,X2) = 1 [U74](X) = 1 [U81](X1,X2) = 1 [U82](X1,X2) = 1 [U83](X) = 1 [U91](X1,X2) = 1 [U92](X) = 0 [__](X1,X2) = 0 [active](X) = 2 [isList](X) = 1 [isNeList](X) = 1 [isNePal](X) = 1 [isPal](X) = 0 [isPalListKind](X) = 1 [isQid](X) = 0 [mark](X) = 2 [a] = 0 [e] = 0 [i] = 0 [nil] = 2 [o] = 0 [tt] = 2 [u] = 2 [ACTIVE](X) = X + 1 [MARK](X) = 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U72(X1,X2)) -> MARK(X1) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = X1 + 2.X2 [U12](X1,X2) = 2.X2 + 2 [U13](X) = X [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U22](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U23](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U24](X1,X2,X3) = 2.X2 + 2.X3 + 2 [U25](X1,X2) = X1 + X2 [U26](X) = 2 [U31](X1,X2) = X1 + 2.X2 [U32](X1,X2) = 2.X2 + 2 [U33](X) = X [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U43](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U44](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U45](X1,X2) = X1 + X2 + 2 [U46](X) = 2 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U52](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U53](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U54](X1,X2,X3) = 2.X2 + 2.X3 + 2 [U55](X1,X2) = X1 + 2.X2 [U56](X) = X [U61](X1,X2) = X2 + 2 [U62](X1,X2) = X2 + 2 [U63](X) = 2 [U71](X1,X2,X3) = 2.X1 + X2 + 2.X3 + 1 [U72](X1,X2) = X1 + 2.X2 + 2 [U73](X1,X2) = X1 + X2 + 2 [U74](X) = X [U81](X1,X2) = X1 + X2 [U82](X1,X2) = X1 + X2 [U83](X) = X [U91](X1,X2) = X1 [U92](X) = X [__](X1,X2) = 2.X1 + X2 + 2 [active](X) = X [isList](X) = 2.X + 2 [isNeList](X) = 2.X + 2 [isNePal](X) = X + 2 [isPal](X) = X + 2 [isPalListKind](X) = 2 [isQid](X) = X + 2 [mark](X) = X [a] = 2 [e] = 1 [i] = 1 [nil] = 2 [o] = 0 [tt] = 2 [u] = 0 [ACTIVE](X) = 2.X + 2 [MARK](X) = 2.X + 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U73(X1,X2)) -> ACTIVE(U73(mark(X1),X2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = 2 [U12](X1,X2) = 2 [U13](X) = 0 [U21](X1,X2,X3) = 1 [U22](X1,X2,X3) = 2 [U23](X1,X2,X3) = 2 [U24](X1,X2,X3) = 1 [U25](X1,X2) = 2 [U26](X) = 1 [U31](X1,X2) = 2 [U32](X1,X2) = 2 [U33](X) = 0 [U41](X1,X2,X3) = 1 [U42](X1,X2,X3) = 2 [U43](X1,X2,X3) = 2 [U44](X1,X2,X3) = 2 [U45](X1,X2) = 1 [U46](X) = 2 [U51](X1,X2,X3) = 2 [U52](X1,X2,X3) = 1 [U53](X1,X2,X3) = 0 [U54](X1,X2,X3) = 0 [U55](X1,X2) = 1 [U56](X) = 1 [U61](X1,X2) = 1 [U62](X1,X2) = 1 [U63](X) = 2 [U71](X1,X2,X3) = 2 [U72](X1,X2) = 2 [U73](X1,X2) = 0 [U74](X) = 2 [U81](X1,X2) = 2 [U82](X1,X2) = 2 [U83](X) = 2 [U91](X1,X2) = 2 [U92](X) = 2 [__](X1,X2) = 2 [active](X) = 2 [isList](X) = 2 [isNeList](X) = 2 [isNePal](X) = 2 [isPal](X) = 0 [isPalListKind](X) = 2 [isQid](X) = 2 [mark](X) = 2 [a] = 0 [e] = 2 [i] = 0 [nil] = 1 [o] = 1 [tt] = 0 [u] = 0 [ACTIVE](X) = X [MARK](X) = 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U73(X1,X2)) -> MARK(X1) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = 2.X2 + 2 [U12](X1,X2) = X1 + 2.X2 [U13](X) = 2 [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U22](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 1 [U23](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 [U24](X1,X2,X3) = 2.X2 + 2.X3 + 2 [U25](X1,X2) = X1 + 2.X2 [U26](X) = X [U31](X1,X2) = 2.X2 + 2 [U32](X1,X2) = 2.X2 + 2 [U33](X) = 2 [U41](X1,X2,X3) = 2.X1 + 2.X3 + 2 [U42](X1,X2,X3) = 2 [U43](X1,X2,X3) = X1 [U44](X1,X2,X3) = 2 [U45](X1,X2) = 2 [U46](X) = 2 [U51](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U52](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U53](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U54](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U55](X1,X2) = X1 + 2.X2 + 2 [U56](X) = 2 [U61](X1,X2) = X1 + X2 [U62](X1,X2) = X1 [U63](X) = 2 [U71](X1,X2,X3) = 2.X1 + 2.X3 + 2 [U72](X1,X2) = 2.X1 + 2.X2 + 2 [U73](X1,X2) = X1 + 2 [U74](X) = X + 2 [U81](X1,X2) = X1 + 2.X2 [U82](X1,X2) = X1 + 2.X2 [U83](X) = X [U91](X1,X2) = X1 [U92](X) = X [__](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 [isPalListKind](X) = 2 [isQid](X) = 2 [mark](X) = X [a] = 1 [e] = 0 [i] = 2 [nil] = 1 [o] = 1 [tt] = 2 [u] = 2 [ACTIVE](X) = 2.X + 2 [MARK](X) = 2.X + 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U74(X)) -> ACTIVE(U74(mark(X))) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = 2 [U12](X1,X2) = 1 [U13](X) = 2 [U21](X1,X2,X3) = 2 [U22](X1,X2,X3) = 0 [U23](X1,X2,X3) = 2 [U24](X1,X2,X3) = 1 [U25](X1,X2) = 0 [U26](X) = 1 [U31](X1,X2) = 2 [U32](X1,X2) = 1 [U33](X) = 2 [U41](X1,X2,X3) = 2 [U42](X1,X2,X3) = 2 [U43](X1,X2,X3) = 2 [U44](X1,X2,X3) = 2 [U45](X1,X2) = 2 [U46](X) = 1 [U51](X1,X2,X3) = 2 [U52](X1,X2,X3) = 2 [U53](X1,X2,X3) = 2 [U54](X1,X2,X3) = 2 [U55](X1,X2) = 2 [U56](X) = 2 [U61](X1,X2) = 2 [U62](X1,X2) = 2 [U63](X) = 2 [U71](X1,X2,X3) = 2 [U72](X1,X2) = 2 [U73](X1,X2) = 1 [U74](X) = 0 [U81](X1,X2) = 1 [U82](X1,X2) = 0 [U83](X) = 1 [U91](X1,X2) = 1 [U92](X) = 0 [__](X1,X2) = 1 [active](X) = 2 [isList](X) = 0 [isNeList](X) = 1 [isNePal](X) = 0 [isPal](X) = 1 [isPalListKind](X) = 1 [isQid](X) = 0 [mark](X) = 2 [a] = 2 [e] = 0 [i] = 2 [nil] = 2 [o] = 2 [tt] = 0 [u] = 2 [ACTIVE](X) = 2.X [MARK](X) = 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U74(X)) -> MARK(X) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = 2.X2 + 2 [U12](X1,X2) = 2.X2 + 2 [U13](X) = X [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U22](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U23](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U24](X1,X2,X3) = X1 + 2.X3 + 2 [U25](X1,X2) = 2.X2 + 2 [U26](X) = 2 [U31](X1,X2) = X1 + 2.X2 [U32](X1,X2) = X2 + 2 [U33](X) = 2 [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U43](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U44](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U45](X1,X2) = X1 + 2.X2 + 2 [U46](X) = X [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U52](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U53](X1,X2,X3) = 2.X1 + 2.X2 + X3 + 2 [U54](X1,X2,X3) = X1 + 2.X2 + X3 + 2 [U55](X1,X2) = X1 + 2 [U56](X) = 2 [U61](X1,X2) = X1 + 2.X2 [U62](X1,X2) = 2.X2 + 2 [U63](X) = 2.X + 2 [U71](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U72](X1,X2) = 2.X1 + 2.X2 + 1 [U73](X1,X2) = X1 + 2 [U74](X) = X + 2 [U81](X1,X2) = X1 + 2.X2 [U82](X1,X2) = X1 + 2.X2 [U83](X) = X [U91](X1,X2) = X1 [U92](X) = X [__](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 [isPalListKind](X) = 2 [isQid](X) = X [mark](X) = X [a] = 2 [e] = 2 [i] = 2 [nil] = 2 [o] = 2 [tt] = 2 [u] = 2 [ACTIVE](X) = X + 2 [MARK](X) = X + 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(U91(tt,V2)) -> MARK(U92(isPalListKind(V2))) ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = 2.X1 + 2 [U12](X1,X2) = 2 [U13](X) = 2 [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 1 [U22](X1,X2,X3) = 2.X2 + 2.X3 + 2 [U23](X1,X2,X3) = 2.X2 + 2.X3 + 2 [U24](X1,X2,X3) = 2.X1 + 2.X2 + 1 [U25](X1,X2) = X1 + 1 [U26](X) = 2 [U31](X1,X2) = 2.X1 + 1 [U32](X1,X2) = 2 [U33](X) = 2 [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = 2.X2 + 2.X3 + 2 [U43](X1,X2,X3) = 2.X2 + 2.X3 + 2 [U44](X1,X2,X3) = 2.X1 + 2.X2 [U45](X1,X2) = X1 [U46](X) = 2 [U51](X1,X2,X3) = 2.X2 + 2.X3 + 2 [U52](X1,X2,X3) = 2.X1 + 2.X3 + 2 [U53](X1,X2,X3) = 2.X3 + 2 [U54](X1,X2,X3) = 2.X1 + 2 [U55](X1,X2) = 2 [U56](X) = 2 [U61](X1,X2) = 2 [U62](X1,X2) = 2 [U63](X) = 2 [U71](X1,X2,X3) = 2 [U72](X1,X2) = 2 [U73](X1,X2) = 2 [U74](X) = 2 [U81](X1,X2) = X1 + X2 + 2 [U82](X1,X2) = X1 + 2 [U83](X) = X [U91](X1,X2) = 2.X1 + X2 + 2 [U92](X) = X + 2 [__](X1,X2) = 2.X1 + X2 + 2 [active](X) = X [isList](X) = 2.X + 2 [isNeList](X) = 2.X + 2 [isNePal](X) = 2 [isPal](X) = 2.X + 2 [isPalListKind](X) = X [isQid](X) = 2.X [mark](X) = X [a] = 2 [e] = 2 [i] = 2 [nil] = 2 [o] = 2 [tt] = 2 [u] = 2 [ACTIVE](X) = 2.X + 2 [MARK](X) = 2.X + 2 Problem 1.44: SCC Processor: -> Pairs: ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Reduction Pair Processor: -> Pairs: ACTIVE(isPalListKind(__(V1,V2))) -> MARK(U91(isPalListKind(V1),V2)) MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) -> Usable rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X1,X2) = 2.X2 + 2 [U12](X1,X2) = X1 + X2 [U13](X) = 2 [U21](X1,X2,X3) = 2.X1 + 2.X2 + X3 [U22](X1,X2,X3) = 2.X1 + X3 [U23](X1,X2,X3) = X3 + 2 [U24](X1,X2,X3) = X3 + 2 [U25](X1,X2) = X2 + 2 [U26](X) = 2 [U31](X1,X2) = 2.X2 + 2 [U32](X1,X2) = 2.X2 + 2 [U33](X) = 2.X [U41](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = X1 + X2 + 2.X3 + 2 [U43](X1,X2,X3) = X2 + X3 + 2 [U44](X1,X2,X3) = X2 + X3 + 2 [U45](X1,X2) = X2 + 2 [U46](X) = 2 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U52](X1,X2,X3) = 2.X1 + 2.X3 + 2 [U53](X1,X2,X3) = 2.X3 + 2 [U54](X1,X2,X3) = 2.X3 + 2 [U55](X1,X2) = 2 [U56](X) = 2 [U61](X1,X2) = 2 [U62](X1,X2) = 2 [U63](X) = 2 [U71](X1,X2,X3) = 2 [U72](X1,X2) = 2 [U73](X1,X2) = 2 [U74](X) = 2 [U81](X1,X2) = X1 + X2 [U82](X1,X2) = X1 [U83](X) = X [U91](X1,X2) = X1 + X2 + 1 [U92](X) = X + 1 [__](X1,X2) = 2.X1 + X2 + 2 [active](X) = X [isList](X) = 2.X + 2 [isNeList](X) = 2.X + 2 [isNePal](X) = 2 [isPal](X) = 2.X + 2 [isPalListKind](X) = X + 2 [isQid](X) = X + 1 [mark](X) = X [a] = 2 [e] = 2 [i] = 1 [nil] = 2 [o] = 2 [tt] = 2 [u] = 2 [ACTIVE](X) = 2.X + 1 [MARK](X) = 2.X + 1 Problem 1.44: SCC Processor: -> Pairs: MARK(U81(X1,X2)) -> ACTIVE(U81(mark(X1),X2)) MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> ACTIVE(U82(mark(X1),X2)) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> ACTIVE(U83(mark(X))) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> ACTIVE(U91(mark(X1),X2)) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> ACTIVE(U92(mark(X))) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2))) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) MARK(isList(X)) -> ACTIVE(isList(X)) MARK(isNeList(X)) -> ACTIVE(isNeList(X)) MARK(isNePal(X)) -> ACTIVE(isNePal(X)) MARK(isPal(X)) -> ACTIVE(isPal(X)) MARK(isPalListKind(X)) -> ACTIVE(isPalListKind(X)) MARK(isQid(X)) -> ACTIVE(isQid(X)) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) ->->-> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) Problem 1.44: Subterm Processor: -> Pairs: MARK(U81(X1,X2)) -> MARK(X1) MARK(U82(X1,X2)) -> MARK(X1) MARK(U83(X)) -> MARK(X) MARK(U91(X1,X2)) -> MARK(X1) MARK(U92(X)) -> MARK(X) MARK(__(X1,X2)) -> MARK(X1) MARK(__(X1,X2)) -> MARK(X2) -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Projection: pi(MARK) = 1 Problem 1.44: SCC Processor: -> Pairs: Empty -> Rules: U11(active(X1),X2) -> U11(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U13(active(X)) -> U13(X) U13(mark(X)) -> U13(X) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U22(active(X1),X2,X3) -> U22(X1,X2,X3) U22(mark(X1),X2,X3) -> U22(X1,X2,X3) U22(X1,active(X2),X3) -> U22(X1,X2,X3) U22(X1,mark(X2),X3) -> U22(X1,X2,X3) U22(X1,X2,active(X3)) -> U22(X1,X2,X3) U22(X1,X2,mark(X3)) -> U22(X1,X2,X3) U23(active(X1),X2,X3) -> U23(X1,X2,X3) U23(mark(X1),X2,X3) -> U23(X1,X2,X3) U23(X1,active(X2),X3) -> U23(X1,X2,X3) U23(X1,mark(X2),X3) -> U23(X1,X2,X3) U23(X1,X2,active(X3)) -> U23(X1,X2,X3) U23(X1,X2,mark(X3)) -> U23(X1,X2,X3) U24(active(X1),X2,X3) -> U24(X1,X2,X3) U24(mark(X1),X2,X3) -> U24(X1,X2,X3) U24(X1,active(X2),X3) -> U24(X1,X2,X3) U24(X1,mark(X2),X3) -> U24(X1,X2,X3) U24(X1,X2,active(X3)) -> U24(X1,X2,X3) U24(X1,X2,mark(X3)) -> U24(X1,X2,X3) U25(active(X1),X2) -> U25(X1,X2) U25(mark(X1),X2) -> U25(X1,X2) U25(X1,active(X2)) -> U25(X1,X2) U25(X1,mark(X2)) -> U25(X1,X2) U26(active(X)) -> U26(X) U26(mark(X)) -> U26(X) U31(active(X1),X2) -> U31(X1,X2) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U33(active(X)) -> U33(X) U33(mark(X)) -> U33(X) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U45(active(X1),X2) -> U45(X1,X2) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U46(active(X)) -> U46(X) U46(mark(X)) -> U46(X) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U52(active(X1),X2,X3) -> U52(X1,X2,X3) U52(mark(X1),X2,X3) -> U52(X1,X2,X3) U52(X1,active(X2),X3) -> U52(X1,X2,X3) U52(X1,mark(X2),X3) -> U52(X1,X2,X3) U52(X1,X2,active(X3)) -> U52(X1,X2,X3) U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) U53(active(X1),X2,X3) -> U53(X1,X2,X3) U53(mark(X1),X2,X3) -> U53(X1,X2,X3) U53(X1,active(X2),X3) -> U53(X1,X2,X3) U53(X1,mark(X2),X3) -> U53(X1,X2,X3) U53(X1,X2,active(X3)) -> U53(X1,X2,X3) U53(X1,X2,mark(X3)) -> U53(X1,X2,X3) U54(active(X1),X2,X3) -> U54(X1,X2,X3) U54(mark(X1),X2,X3) -> U54(X1,X2,X3) U54(X1,active(X2),X3) -> U54(X1,X2,X3) U54(X1,mark(X2),X3) -> U54(X1,X2,X3) U54(X1,X2,active(X3)) -> U54(X1,X2,X3) U54(X1,X2,mark(X3)) -> U54(X1,X2,X3) U55(active(X1),X2) -> U55(X1,X2) U55(mark(X1),X2) -> U55(X1,X2) U55(X1,active(X2)) -> U55(X1,X2) U55(X1,mark(X2)) -> U55(X1,X2) U56(active(X)) -> U56(X) U56(mark(X)) -> U56(X) U61(active(X1),X2) -> U61(X1,X2) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U63(active(X)) -> U63(X) U63(mark(X)) -> U63(X) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U72(active(X1),X2) -> U72(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U73(active(X1),X2) -> U73(X1,X2) U73(mark(X1),X2) -> U73(X1,X2) U73(X1,active(X2)) -> U73(X1,X2) U73(X1,mark(X2)) -> U73(X1,X2) U74(active(X)) -> U74(X) U74(mark(X)) -> U74(X) U81(active(X1),X2) -> U81(X1,X2) U81(mark(X1),X2) -> U81(X1,X2) U81(X1,active(X2)) -> U81(X1,X2) U81(X1,mark(X2)) -> U81(X1,X2) U82(active(X1),X2) -> U82(X1,X2) U82(mark(X1),X2) -> U82(X1,X2) U82(X1,active(X2)) -> U82(X1,X2) U82(X1,mark(X2)) -> U82(X1,X2) U83(active(X)) -> U83(X) U83(mark(X)) -> U83(X) U91(active(X1),X2) -> U91(X1,X2) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U92(active(X)) -> U92(X) U92(mark(X)) -> U92(X) __(active(X1),X2) -> __(X1,X2) __(mark(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) active(U11(tt,V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt,V)) -> mark(U13(isNeList(V))) active(U13(tt)) -> mark(tt) active(U21(tt,V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt,V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt,V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt,V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt,V2)) -> mark(U26(isList(V2))) active(U26(tt)) -> mark(tt) active(U31(tt,V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt,V)) -> mark(U33(isQid(V))) active(U33(tt)) -> mark(tt) active(U41(tt,V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt,V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt,V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt,V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt,V2)) -> mark(U46(isNeList(V2))) active(U46(tt)) -> mark(tt) active(U51(tt,V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt,V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt,V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt,V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt,V2)) -> mark(U56(isList(V2))) active(U56(tt)) -> mark(tt) active(U61(tt,V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt,V)) -> mark(U63(isQid(V))) active(U63(tt)) -> mark(tt) active(U71(tt,I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt,P)) -> mark(U73(isPal(P),P)) active(U73(tt,P)) -> mark(U74(isPalListKind(P))) active(U74(tt)) -> mark(tt) active(U81(tt,V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt,V)) -> mark(U83(isNePal(V))) active(U83(tt)) -> mark(tt) active(U91(tt,V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt)) -> mark(tt) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(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(active(X)) -> isList(X) isList(mark(X)) -> isList(X) isNeList(active(X)) -> isNeList(X) isNeList(mark(X)) -> isNeList(X) isNePal(active(X)) -> isNePal(X) isNePal(mark(X)) -> isNePal(X) isPal(active(X)) -> isPal(X) isPal(mark(X)) -> isPal(X) isPalListKind(active(X)) -> isPalListKind(X) isPalListKind(mark(X)) -> isPalListKind(X) isQid(active(X)) -> isQid(X) isQid(mark(X)) -> isQid(X) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U13(X)) -> active(U13(mark(X))) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3)) mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3)) mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3)) mark(U25(X1,X2)) -> active(U25(mark(X1),X2)) mark(U26(X)) -> active(U26(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3)) mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3)) mark(U55(X1,X2)) -> active(U55(mark(X1),X2)) mark(U56(X)) -> active(U56(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(U63(X)) -> active(U63(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U73(X1,X2)) -> active(U73(mark(X1),X2)) mark(U74(X)) -> active(U74(mark(X))) mark(U81(X1,X2)) -> active(U81(mark(X1),X2)) mark(U82(X1,X2)) -> active(U82(mark(X1),X2)) mark(U83(X)) -> active(U83(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isQid(X)) -> active(isQid(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(nil) -> active(nil) mark(o) -> active(o) mark(tt) -> active(tt) mark(u) -> active(u) ->Strongly Connected Components: There is no strongly connected component The problem is finite.