/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- Error at 1: Unexpected token '>=', 'benchmark' expected. syntax error rm: cannot remove ‘/tmp/muTerm1804289383846930886.in.dec’: Operation not permitted rm: cannot remove ‘/tmp/muTerm1804289383846930886.in.form’: Operation not permitted Error at 1: Unexpected token '>=', 'benchmark' expected. syntax error rm: cannot remove ‘/tmp/muTerm1957747793424238335.in.dec’: Operation not permitted rm: cannot remove ‘/tmp/muTerm1957747793424238335.in.form’: Operation not permitted Error at 1: Unexpected token '>=', 'benchmark' expected. syntax error rm: cannot remove ‘/tmp/muTerm5965166491189641421.in.dec’: Operation not permitted rm: cannot remove ‘/tmp/muTerm5965166491189641421.in.form’: Operation not permitted Error at 1: Unexpected token '>=', 'benchmark' expected. syntax error rm: cannot remove ‘/tmp/muTerm7833686901102520059.in.dec’: Operation not permitted rm: cannot remove ‘/tmp/muTerm7833686901102520059.in.form’: Operation not permitted Error at 1: Unexpected token '>=', 'benchmark' expected. syntax error rm: cannot remove ‘/tmp/muTerm13651805401540383426.in.dec’: Operation not permitted rm: cannot remove ‘/tmp/muTerm13651805401540383426.in.form’: Operation not permitted Error at 1: Unexpected token '>=', 'benchmark' expected. syntax error rm: cannot remove ‘/tmp/muTerm35005211521595368.in.dec’: Operation not permitted rm: cannot remove ‘/tmp/muTerm35005211521595368.in.form’: Operation not permitted Error at 1: Unexpected token '>=', 'benchmark' expected. syntax error rm: cannot remove ‘/tmp/muTerm336465782861021530.in.dec’: Operation not permitted rm: cannot remove ‘/tmp/muTerm336465782861021530.in.form’: Operation not permitted Error at 1: Unexpected token '>=', 'benchmark' expected. syntax error rm: cannot remove ‘/tmp/muTerm2145174067468703135.in.dec’: Operation not permitted rm: cannot remove ‘/tmp/muTerm2145174067468703135.in.form’: Operation not permitted Error at 1: Unexpected token '>=', 'benchmark' expected. syntax error rm: cannot remove ‘/tmp/muTerm1315634022635723058.in.dec’: Operation not permitted rm: cannot remove ‘/tmp/muTerm1315634022635723058.in.form’: Operation not permitted Error at 1: Unexpected token '>=', 'benchmark' expected. syntax error rm: cannot remove ‘/tmp/muTerm10599613932089018456.in.dec’: Operation not permitted rm: cannot remove ‘/tmp/muTerm10599613932089018456.in.form’: Operation not permitted Error at 1: Unexpected token '>=', 'benchmark' expected. syntax error rm: cannot remove ‘/tmp/muTerm11311762291653377373.in.dec’: Operation not permitted rm: cannot remove ‘/tmp/muTerm11311762291653377373.in.form’: Operation not permitted Error at 1: Unexpected token '>=', 'benchmark' expected. syntax error rm: cannot remove ‘/tmp/muTerm608413784756898537.in.dec’: Operation not permitted rm: cannot remove ‘/tmp/muTerm608413784756898537.in.form’: Operation not permitted Error at 1: Unexpected token '>=', 'benchmark' expected. syntax error rm: cannot remove ‘/tmp/muTerm1497983152038664370.in.dec’: Operation not permitted rm: cannot remove ‘/tmp/muTerm1497983152038664370.in.form’: Operation not permitted Error at 1: Unexpected token '>=', 'benchmark' expected. syntax error rm: cannot remove ‘/tmp/muTerm4127760911424268980.in.dec’: Operation not permitted rm: cannot remove ‘/tmp/muTerm4127760911424268980.in.form’: Operation not permitted Error at 1: Unexpected token '>=', 'benchmark' expected. syntax error rm: cannot remove ‘/tmp/muTerm13780686242999170.in.dec’: Operation not permitted rm: cannot remove ‘/tmp/muTerm13780686242999170.in.form’: Operation not permitted YES Problem 1: (VAR I P V V1 V2 X X1 X2 Y Z) (RULES U11(tt,V) -> U12(isPalListKind(activate(V)),activate(V)) U12(tt,V) -> U13(isNeList(activate(V))) U13(tt) -> tt U21(tt,V1,V2) -> U22(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22(tt,V1,V2) -> U23(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23(tt,V1,V2) -> U24(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24(tt,V1,V2) -> U25(isList(activate(V1)),activate(V2)) U25(tt,V2) -> U26(isList(activate(V2))) U26(tt) -> tt U31(tt,V) -> U32(isPalListKind(activate(V)),activate(V)) U32(tt,V) -> U33(isQid(activate(V))) U33(tt) -> tt U41(tt,V1,V2) -> U42(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42(tt,V1,V2) -> U43(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43(tt,V1,V2) -> U44(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44(tt,V1,V2) -> U45(isList(activate(V1)),activate(V2)) U45(tt,V2) -> U46(isNeList(activate(V2))) U46(tt) -> tt U51(tt,V1,V2) -> U52(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52(tt,V1,V2) -> U53(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53(tt,V1,V2) -> U54(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54(tt,V1,V2) -> U55(isNeList(activate(V1)),activate(V2)) U55(tt,V2) -> U56(isList(activate(V2))) U56(tt) -> tt U61(tt,V) -> U62(isPalListKind(activate(V)),activate(V)) U62(tt,V) -> U63(isQid(activate(V))) U63(tt) -> tt U71(tt,I,P) -> U72(isPalListKind(activate(I)),activate(P)) U72(tt,P) -> U73(isPal(activate(P)),activate(P)) U73(tt,P) -> U74(isPalListKind(activate(P))) U74(tt) -> tt U81(tt,V) -> U82(isPalListKind(activate(V)),activate(V)) U82(tt,V) -> U83(isNePal(activate(V))) U83(tt) -> tt U91(tt,V2) -> U92(isPalListKind(activate(V2))) U92(tt) -> tt __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil,X) -> X __(X,nil) -> X __(X1,X2) -> n____(X1,X2) a -> n__a activate(n____(X1,X2)) -> __(X1,X2) activate(n__a) -> a activate(n__e) -> e activate(n__i) -> i activate(n__nil) -> nil activate(n__o) -> o activate(n__u) -> u activate(X) -> X e -> n__e i -> n__i isList(n____(V1,V2)) -> U21(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList(n__nil) -> tt isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,__(P,I))) -> U71(isQid(activate(I)),activate(I),activate(P)) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isPal(n__nil) -> tt isPal(V) -> U81(isPalListKind(activate(V)),activate(V)) isPalListKind(n____(V1,V2)) -> U91(isPalListKind(activate(V1)),activate(V2)) isPalListKind(n__a) -> tt isPalListKind(n__e) -> tt isPalListKind(n__i) -> tt isPalListKind(n__nil) -> tt isPalListKind(n__o) -> tt isPalListKind(n__u) -> tt isQid(n__a) -> tt isQid(n__e) -> tt isQid(n__i) -> tt isQid(n__o) -> tt isQid(n__u) -> tt nil -> n__nil o -> n__o u -> n__u ) Problem 1: Dependency Pairs Processor: -> Pairs: U11#(tt,V) -> U12#(isPalListKind(activate(V)),activate(V)) U11#(tt,V) -> ACTIVATE(V) U11#(tt,V) -> ISPALLISTKIND(activate(V)) U12#(tt,V) -> U13#(isNeList(activate(V))) U12#(tt,V) -> ACTIVATE(V) U12#(tt,V) -> ISNELIST(activate(V)) U21#(tt,V1,V2) -> U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)) U21#(tt,V1,V2) -> ACTIVATE(V1) U21#(tt,V1,V2) -> ACTIVATE(V2) U21#(tt,V1,V2) -> ISPALLISTKIND(activate(V1)) U22#(tt,V1,V2) -> U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U22#(tt,V1,V2) -> ACTIVATE(V1) U22#(tt,V1,V2) -> ACTIVATE(V2) U22#(tt,V1,V2) -> ISPALLISTKIND(activate(V2)) U23#(tt,V1,V2) -> U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23#(tt,V1,V2) -> ACTIVATE(V1) U23#(tt,V1,V2) -> ACTIVATE(V2) U23#(tt,V1,V2) -> ISPALLISTKIND(activate(V2)) U24#(tt,V1,V2) -> U25#(isList(activate(V1)),activate(V2)) U24#(tt,V1,V2) -> ACTIVATE(V1) U24#(tt,V1,V2) -> ACTIVATE(V2) U24#(tt,V1,V2) -> ISLIST(activate(V1)) U25#(tt,V2) -> U26#(isList(activate(V2))) U25#(tt,V2) -> ACTIVATE(V2) U25#(tt,V2) -> ISLIST(activate(V2)) U31#(tt,V) -> U32#(isPalListKind(activate(V)),activate(V)) U31#(tt,V) -> ACTIVATE(V) U31#(tt,V) -> ISPALLISTKIND(activate(V)) U32#(tt,V) -> U33#(isQid(activate(V))) U32#(tt,V) -> ACTIVATE(V) U32#(tt,V) -> ISQID(activate(V)) U41#(tt,V1,V2) -> U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)) U41#(tt,V1,V2) -> ACTIVATE(V1) U41#(tt,V1,V2) -> ACTIVATE(V2) U41#(tt,V1,V2) -> ISPALLISTKIND(activate(V1)) U42#(tt,V1,V2) -> U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U42#(tt,V1,V2) -> ACTIVATE(V1) U42#(tt,V1,V2) -> ACTIVATE(V2) U42#(tt,V1,V2) -> ISPALLISTKIND(activate(V2)) U43#(tt,V1,V2) -> U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43#(tt,V1,V2) -> ACTIVATE(V1) U43#(tt,V1,V2) -> ACTIVATE(V2) U43#(tt,V1,V2) -> ISPALLISTKIND(activate(V2)) U44#(tt,V1,V2) -> U45#(isList(activate(V1)),activate(V2)) U44#(tt,V1,V2) -> ACTIVATE(V1) U44#(tt,V1,V2) -> ACTIVATE(V2) U44#(tt,V1,V2) -> ISLIST(activate(V1)) U45#(tt,V2) -> U46#(isNeList(activate(V2))) U45#(tt,V2) -> ACTIVATE(V2) U45#(tt,V2) -> ISNELIST(activate(V2)) U51#(tt,V1,V2) -> U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)) U51#(tt,V1,V2) -> ACTIVATE(V1) U51#(tt,V1,V2) -> ACTIVATE(V2) U51#(tt,V1,V2) -> ISPALLISTKIND(activate(V1)) U52#(tt,V1,V2) -> U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U52#(tt,V1,V2) -> ACTIVATE(V1) U52#(tt,V1,V2) -> ACTIVATE(V2) U52#(tt,V1,V2) -> ISPALLISTKIND(activate(V2)) U53#(tt,V1,V2) -> U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53#(tt,V1,V2) -> ACTIVATE(V1) U53#(tt,V1,V2) -> ACTIVATE(V2) U53#(tt,V1,V2) -> ISPALLISTKIND(activate(V2)) U54#(tt,V1,V2) -> U55#(isNeList(activate(V1)),activate(V2)) U54#(tt,V1,V2) -> ACTIVATE(V1) U54#(tt,V1,V2) -> ACTIVATE(V2) U54#(tt,V1,V2) -> ISNELIST(activate(V1)) U55#(tt,V2) -> U56#(isList(activate(V2))) U55#(tt,V2) -> ACTIVATE(V2) U55#(tt,V2) -> ISLIST(activate(V2)) U61#(tt,V) -> U62#(isPalListKind(activate(V)),activate(V)) U61#(tt,V) -> ACTIVATE(V) U61#(tt,V) -> ISPALLISTKIND(activate(V)) U62#(tt,V) -> U63#(isQid(activate(V))) U62#(tt,V) -> ACTIVATE(V) U62#(tt,V) -> ISQID(activate(V)) U71#(tt,I,P) -> U72#(isPalListKind(activate(I)),activate(P)) U71#(tt,I,P) -> ACTIVATE(I) U71#(tt,I,P) -> ACTIVATE(P) U71#(tt,I,P) -> ISPALLISTKIND(activate(I)) U72#(tt,P) -> U73#(isPal(activate(P)),activate(P)) U72#(tt,P) -> ACTIVATE(P) U72#(tt,P) -> ISPAL(activate(P)) U73#(tt,P) -> U74#(isPalListKind(activate(P))) U73#(tt,P) -> ACTIVATE(P) U73#(tt,P) -> ISPALLISTKIND(activate(P)) U81#(tt,V) -> U82#(isPalListKind(activate(V)),activate(V)) U81#(tt,V) -> ACTIVATE(V) U81#(tt,V) -> ISPALLISTKIND(activate(V)) U82#(tt,V) -> U83#(isNePal(activate(V))) U82#(tt,V) -> ACTIVATE(V) U82#(tt,V) -> ISNEPAL(activate(V)) U91#(tt,V2) -> U92#(isPalListKind(activate(V2))) U91#(tt,V2) -> ACTIVATE(V2) U91#(tt,V2) -> ISPALLISTKIND(activate(V2)) __#(__(X,Y),Z) -> __#(X,__(Y,Z)) __#(__(X,Y),Z) -> __#(Y,Z) ACTIVATE(n____(X1,X2)) -> __#(X1,X2) ACTIVATE(n__a) -> A ACTIVATE(n__e) -> E ACTIVATE(n__i) -> I ACTIVATE(n__nil) -> NIL ACTIVATE(n__o) -> O ACTIVATE(n__u) -> U ISLIST(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ISLIST(n____(V1,V2)) -> ACTIVATE(V1) ISLIST(n____(V1,V2)) -> ACTIVATE(V2) ISLIST(n____(V1,V2)) -> ISPALLISTKIND(activate(V1)) ISLIST(V) -> U11#(isPalListKind(activate(V)),activate(V)) ISLIST(V) -> ACTIVATE(V) ISLIST(V) -> ISPALLISTKIND(activate(V)) ISNELIST(n____(V1,V2)) -> U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ISNELIST(n____(V1,V2)) -> U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ISNELIST(n____(V1,V2)) -> ACTIVATE(V1) ISNELIST(n____(V1,V2)) -> ACTIVATE(V2) ISNELIST(n____(V1,V2)) -> ISPALLISTKIND(activate(V1)) ISNELIST(V) -> U31#(isPalListKind(activate(V)),activate(V)) ISNELIST(V) -> ACTIVATE(V) ISNELIST(V) -> ISPALLISTKIND(activate(V)) ISNEPAL(n____(I,__(P,I))) -> U71#(isQid(activate(I)),activate(I),activate(P)) ISNEPAL(n____(I,__(P,I))) -> ACTIVATE(I) ISNEPAL(n____(I,__(P,I))) -> ACTIVATE(P) ISNEPAL(n____(I,__(P,I))) -> ISQID(activate(I)) ISNEPAL(V) -> U61#(isPalListKind(activate(V)),activate(V)) ISNEPAL(V) -> ACTIVATE(V) ISNEPAL(V) -> ISPALLISTKIND(activate(V)) ISPAL(V) -> U81#(isPalListKind(activate(V)),activate(V)) ISPAL(V) -> ACTIVATE(V) ISPAL(V) -> ISPALLISTKIND(activate(V)) ISPALLISTKIND(n____(V1,V2)) -> U91#(isPalListKind(activate(V1)),activate(V2)) ISPALLISTKIND(n____(V1,V2)) -> ACTIVATE(V1) ISPALLISTKIND(n____(V1,V2)) -> ACTIVATE(V2) ISPALLISTKIND(n____(V1,V2)) -> ISPALLISTKIND(activate(V1)) -> Rules: U11(tt,V) -> U12(isPalListKind(activate(V)),activate(V)) U12(tt,V) -> U13(isNeList(activate(V))) U13(tt) -> tt U21(tt,V1,V2) -> U22(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22(tt,V1,V2) -> U23(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23(tt,V1,V2) -> U24(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24(tt,V1,V2) -> U25(isList(activate(V1)),activate(V2)) U25(tt,V2) -> U26(isList(activate(V2))) U26(tt) -> tt U31(tt,V) -> U32(isPalListKind(activate(V)),activate(V)) U32(tt,V) -> U33(isQid(activate(V))) U33(tt) -> tt U41(tt,V1,V2) -> U42(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42(tt,V1,V2) -> U43(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43(tt,V1,V2) -> U44(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44(tt,V1,V2) -> U45(isList(activate(V1)),activate(V2)) U45(tt,V2) -> U46(isNeList(activate(V2))) U46(tt) -> tt U51(tt,V1,V2) -> U52(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52(tt,V1,V2) -> U53(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53(tt,V1,V2) -> U54(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54(tt,V1,V2) -> U55(isNeList(activate(V1)),activate(V2)) U55(tt,V2) -> U56(isList(activate(V2))) U56(tt) -> tt U61(tt,V) -> U62(isPalListKind(activate(V)),activate(V)) U62(tt,V) -> U63(isQid(activate(V))) U63(tt) -> tt U71(tt,I,P) -> U72(isPalListKind(activate(I)),activate(P)) U72(tt,P) -> U73(isPal(activate(P)),activate(P)) U73(tt,P) -> U74(isPalListKind(activate(P))) U74(tt) -> tt U81(tt,V) -> U82(isPalListKind(activate(V)),activate(V)) U82(tt,V) -> U83(isNePal(activate(V))) U83(tt) -> tt U91(tt,V2) -> U92(isPalListKind(activate(V2))) U92(tt) -> tt __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil,X) -> X __(X,nil) -> X __(X1,X2) -> n____(X1,X2) a -> n__a activate(n____(X1,X2)) -> __(X1,X2) activate(n__a) -> a activate(n__e) -> e activate(n__i) -> i activate(n__nil) -> nil activate(n__o) -> o activate(n__u) -> u activate(X) -> X e -> n__e i -> n__i isList(n____(V1,V2)) -> U21(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList(n__nil) -> tt isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,__(P,I))) -> U71(isQid(activate(I)),activate(I),activate(P)) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isPal(n__nil) -> tt isPal(V) -> U81(isPalListKind(activate(V)),activate(V)) isPalListKind(n____(V1,V2)) -> U91(isPalListKind(activate(V1)),activate(V2)) isPalListKind(n__a) -> tt isPalListKind(n__e) -> tt isPalListKind(n__i) -> tt isPalListKind(n__nil) -> tt isPalListKind(n__o) -> tt isPalListKind(n__u) -> tt isQid(n__a) -> tt isQid(n__e) -> tt isQid(n__i) -> tt isQid(n__o) -> tt isQid(n__u) -> tt nil -> n__nil o -> n__o u -> n__u Problem 1: SCC Processor: -> Pairs: U11#(tt,V) -> U12#(isPalListKind(activate(V)),activate(V)) U11#(tt,V) -> ACTIVATE(V) U11#(tt,V) -> ISPALLISTKIND(activate(V)) U12#(tt,V) -> U13#(isNeList(activate(V))) U12#(tt,V) -> ACTIVATE(V) U12#(tt,V) -> ISNELIST(activate(V)) U21#(tt,V1,V2) -> U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)) U21#(tt,V1,V2) -> ACTIVATE(V1) U21#(tt,V1,V2) -> ACTIVATE(V2) U21#(tt,V1,V2) -> ISPALLISTKIND(activate(V1)) U22#(tt,V1,V2) -> U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U22#(tt,V1,V2) -> ACTIVATE(V1) U22#(tt,V1,V2) -> ACTIVATE(V2) U22#(tt,V1,V2) -> ISPALLISTKIND(activate(V2)) U23#(tt,V1,V2) -> U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23#(tt,V1,V2) -> ACTIVATE(V1) U23#(tt,V1,V2) -> ACTIVATE(V2) U23#(tt,V1,V2) -> ISPALLISTKIND(activate(V2)) U24#(tt,V1,V2) -> U25#(isList(activate(V1)),activate(V2)) U24#(tt,V1,V2) -> ACTIVATE(V1) U24#(tt,V1,V2) -> ACTIVATE(V2) U24#(tt,V1,V2) -> ISLIST(activate(V1)) U25#(tt,V2) -> U26#(isList(activate(V2))) U25#(tt,V2) -> ACTIVATE(V2) U25#(tt,V2) -> ISLIST(activate(V2)) U31#(tt,V) -> U32#(isPalListKind(activate(V)),activate(V)) U31#(tt,V) -> ACTIVATE(V) U31#(tt,V) -> ISPALLISTKIND(activate(V)) U32#(tt,V) -> U33#(isQid(activate(V))) U32#(tt,V) -> ACTIVATE(V) U32#(tt,V) -> ISQID(activate(V)) U41#(tt,V1,V2) -> U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)) U41#(tt,V1,V2) -> ACTIVATE(V1) U41#(tt,V1,V2) -> ACTIVATE(V2) U41#(tt,V1,V2) -> ISPALLISTKIND(activate(V1)) U42#(tt,V1,V2) -> U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U42#(tt,V1,V2) -> ACTIVATE(V1) U42#(tt,V1,V2) -> ACTIVATE(V2) U42#(tt,V1,V2) -> ISPALLISTKIND(activate(V2)) U43#(tt,V1,V2) -> U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43#(tt,V1,V2) -> ACTIVATE(V1) U43#(tt,V1,V2) -> ACTIVATE(V2) U43#(tt,V1,V2) -> ISPALLISTKIND(activate(V2)) U44#(tt,V1,V2) -> U45#(isList(activate(V1)),activate(V2)) U44#(tt,V1,V2) -> ACTIVATE(V1) U44#(tt,V1,V2) -> ACTIVATE(V2) U44#(tt,V1,V2) -> ISLIST(activate(V1)) U45#(tt,V2) -> U46#(isNeList(activate(V2))) U45#(tt,V2) -> ACTIVATE(V2) U45#(tt,V2) -> ISNELIST(activate(V2)) U51#(tt,V1,V2) -> U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)) U51#(tt,V1,V2) -> ACTIVATE(V1) U51#(tt,V1,V2) -> ACTIVATE(V2) U51#(tt,V1,V2) -> ISPALLISTKIND(activate(V1)) U52#(tt,V1,V2) -> U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U52#(tt,V1,V2) -> ACTIVATE(V1) U52#(tt,V1,V2) -> ACTIVATE(V2) U52#(tt,V1,V2) -> ISPALLISTKIND(activate(V2)) U53#(tt,V1,V2) -> U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53#(tt,V1,V2) -> ACTIVATE(V1) U53#(tt,V1,V2) -> ACTIVATE(V2) U53#(tt,V1,V2) -> ISPALLISTKIND(activate(V2)) U54#(tt,V1,V2) -> U55#(isNeList(activate(V1)),activate(V2)) U54#(tt,V1,V2) -> ACTIVATE(V1) U54#(tt,V1,V2) -> ACTIVATE(V2) U54#(tt,V1,V2) -> ISNELIST(activate(V1)) U55#(tt,V2) -> U56#(isList(activate(V2))) U55#(tt,V2) -> ACTIVATE(V2) U55#(tt,V2) -> ISLIST(activate(V2)) U61#(tt,V) -> U62#(isPalListKind(activate(V)),activate(V)) U61#(tt,V) -> ACTIVATE(V) U61#(tt,V) -> ISPALLISTKIND(activate(V)) U62#(tt,V) -> U63#(isQid(activate(V))) U62#(tt,V) -> ACTIVATE(V) U62#(tt,V) -> ISQID(activate(V)) U71#(tt,I,P) -> U72#(isPalListKind(activate(I)),activate(P)) U71#(tt,I,P) -> ACTIVATE(I) U71#(tt,I,P) -> ACTIVATE(P) U71#(tt,I,P) -> ISPALLISTKIND(activate(I)) U72#(tt,P) -> U73#(isPal(activate(P)),activate(P)) U72#(tt,P) -> ACTIVATE(P) U72#(tt,P) -> ISPAL(activate(P)) U73#(tt,P) -> U74#(isPalListKind(activate(P))) U73#(tt,P) -> ACTIVATE(P) U73#(tt,P) -> ISPALLISTKIND(activate(P)) U81#(tt,V) -> U82#(isPalListKind(activate(V)),activate(V)) U81#(tt,V) -> ACTIVATE(V) U81#(tt,V) -> ISPALLISTKIND(activate(V)) U82#(tt,V) -> U83#(isNePal(activate(V))) U82#(tt,V) -> ACTIVATE(V) U82#(tt,V) -> ISNEPAL(activate(V)) U91#(tt,V2) -> U92#(isPalListKind(activate(V2))) U91#(tt,V2) -> ACTIVATE(V2) U91#(tt,V2) -> ISPALLISTKIND(activate(V2)) __#(__(X,Y),Z) -> __#(X,__(Y,Z)) __#(__(X,Y),Z) -> __#(Y,Z) ACTIVATE(n____(X1,X2)) -> __#(X1,X2) ACTIVATE(n__a) -> A ACTIVATE(n__e) -> E ACTIVATE(n__i) -> I ACTIVATE(n__nil) -> NIL ACTIVATE(n__o) -> O ACTIVATE(n__u) -> U ISLIST(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ISLIST(n____(V1,V2)) -> ACTIVATE(V1) ISLIST(n____(V1,V2)) -> ACTIVATE(V2) ISLIST(n____(V1,V2)) -> ISPALLISTKIND(activate(V1)) ISLIST(V) -> U11#(isPalListKind(activate(V)),activate(V)) ISLIST(V) -> ACTIVATE(V) ISLIST(V) -> ISPALLISTKIND(activate(V)) ISNELIST(n____(V1,V2)) -> U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ISNELIST(n____(V1,V2)) -> U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ISNELIST(n____(V1,V2)) -> ACTIVATE(V1) ISNELIST(n____(V1,V2)) -> ACTIVATE(V2) ISNELIST(n____(V1,V2)) -> ISPALLISTKIND(activate(V1)) ISNELIST(V) -> U31#(isPalListKind(activate(V)),activate(V)) ISNELIST(V) -> ACTIVATE(V) ISNELIST(V) -> ISPALLISTKIND(activate(V)) ISNEPAL(n____(I,__(P,I))) -> U71#(isQid(activate(I)),activate(I),activate(P)) ISNEPAL(n____(I,__(P,I))) -> ACTIVATE(I) ISNEPAL(n____(I,__(P,I))) -> ACTIVATE(P) ISNEPAL(n____(I,__(P,I))) -> ISQID(activate(I)) ISNEPAL(V) -> U61#(isPalListKind(activate(V)),activate(V)) ISNEPAL(V) -> ACTIVATE(V) ISNEPAL(V) -> ISPALLISTKIND(activate(V)) ISPAL(V) -> U81#(isPalListKind(activate(V)),activate(V)) ISPAL(V) -> ACTIVATE(V) ISPAL(V) -> ISPALLISTKIND(activate(V)) ISPALLISTKIND(n____(V1,V2)) -> U91#(isPalListKind(activate(V1)),activate(V2)) ISPALLISTKIND(n____(V1,V2)) -> ACTIVATE(V1) ISPALLISTKIND(n____(V1,V2)) -> ACTIVATE(V2) ISPALLISTKIND(n____(V1,V2)) -> ISPALLISTKIND(activate(V1)) -> Rules: U11(tt,V) -> U12(isPalListKind(activate(V)),activate(V)) U12(tt,V) -> U13(isNeList(activate(V))) U13(tt) -> tt U21(tt,V1,V2) -> U22(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22(tt,V1,V2) -> U23(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23(tt,V1,V2) -> U24(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24(tt,V1,V2) -> U25(isList(activate(V1)),activate(V2)) U25(tt,V2) -> U26(isList(activate(V2))) U26(tt) -> tt U31(tt,V) -> U32(isPalListKind(activate(V)),activate(V)) U32(tt,V) -> U33(isQid(activate(V))) U33(tt) -> tt U41(tt,V1,V2) -> U42(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42(tt,V1,V2) -> U43(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43(tt,V1,V2) -> U44(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44(tt,V1,V2) -> U45(isList(activate(V1)),activate(V2)) U45(tt,V2) -> U46(isNeList(activate(V2))) U46(tt) -> tt U51(tt,V1,V2) -> U52(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52(tt,V1,V2) -> U53(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53(tt,V1,V2) -> U54(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54(tt,V1,V2) -> U55(isNeList(activate(V1)),activate(V2)) U55(tt,V2) -> U56(isList(activate(V2))) U56(tt) -> tt U61(tt,V) -> U62(isPalListKind(activate(V)),activate(V)) U62(tt,V) -> U63(isQid(activate(V))) U63(tt) -> tt U71(tt,I,P) -> U72(isPalListKind(activate(I)),activate(P)) U72(tt,P) -> U73(isPal(activate(P)),activate(P)) U73(tt,P) -> U74(isPalListKind(activate(P))) U74(tt) -> tt U81(tt,V) -> U82(isPalListKind(activate(V)),activate(V)) U82(tt,V) -> U83(isNePal(activate(V))) U83(tt) -> tt U91(tt,V2) -> U92(isPalListKind(activate(V2))) U92(tt) -> tt __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil,X) -> X __(X,nil) -> X __(X1,X2) -> n____(X1,X2) a -> n__a activate(n____(X1,X2)) -> __(X1,X2) activate(n__a) -> a activate(n__e) -> e activate(n__i) -> i activate(n__nil) -> nil activate(n__o) -> o activate(n__u) -> u activate(X) -> X e -> n__e i -> n__i isList(n____(V1,V2)) -> U21(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList(n__nil) -> tt isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,__(P,I))) -> U71(isQid(activate(I)),activate(I),activate(P)) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isPal(n__nil) -> tt isPal(V) -> U81(isPalListKind(activate(V)),activate(V)) isPalListKind(n____(V1,V2)) -> U91(isPalListKind(activate(V1)),activate(V2)) isPalListKind(n__a) -> tt isPalListKind(n__e) -> tt isPalListKind(n__i) -> tt isPalListKind(n__nil) -> tt isPalListKind(n__o) -> tt isPalListKind(n__u) -> tt isQid(n__a) -> tt isQid(n__e) -> tt isQid(n__i) -> tt isQid(n__o) -> tt isQid(n__u) -> tt nil -> n__nil o -> n__o u -> n__u ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: __#(__(X,Y),Z) -> __#(X,__(Y,Z)) __#(__(X,Y),Z) -> __#(Y,Z) ->->-> Rules: U11(tt,V) -> U12(isPalListKind(activate(V)),activate(V)) U12(tt,V) -> U13(isNeList(activate(V))) U13(tt) -> tt U21(tt,V1,V2) -> U22(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22(tt,V1,V2) -> U23(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23(tt,V1,V2) -> U24(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24(tt,V1,V2) -> U25(isList(activate(V1)),activate(V2)) U25(tt,V2) -> U26(isList(activate(V2))) U26(tt) -> tt U31(tt,V) -> U32(isPalListKind(activate(V)),activate(V)) U32(tt,V) -> U33(isQid(activate(V))) U33(tt) -> tt U41(tt,V1,V2) -> U42(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42(tt,V1,V2) -> U43(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43(tt,V1,V2) -> U44(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44(tt,V1,V2) -> U45(isList(activate(V1)),activate(V2)) U45(tt,V2) -> U46(isNeList(activate(V2))) U46(tt) -> tt U51(tt,V1,V2) -> U52(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52(tt,V1,V2) -> U53(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53(tt,V1,V2) -> U54(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54(tt,V1,V2) -> U55(isNeList(activate(V1)),activate(V2)) U55(tt,V2) -> U56(isList(activate(V2))) U56(tt) -> tt U61(tt,V) -> U62(isPalListKind(activate(V)),activate(V)) U62(tt,V) -> U63(isQid(activate(V))) U63(tt) -> tt U71(tt,I,P) -> U72(isPalListKind(activate(I)),activate(P)) U72(tt,P) -> U73(isPal(activate(P)),activate(P)) U73(tt,P) -> U74(isPalListKind(activate(P))) U74(tt) -> tt U81(tt,V) -> U82(isPalListKind(activate(V)),activate(V)) U82(tt,V) -> U83(isNePal(activate(V))) U83(tt) -> tt U91(tt,V2) -> U92(isPalListKind(activate(V2))) U92(tt) -> tt __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil,X) -> X __(X,nil) -> X __(X1,X2) -> n____(X1,X2) a -> n__a activate(n____(X1,X2)) -> __(X1,X2) activate(n__a) -> a activate(n__e) -> e activate(n__i) -> i activate(n__nil) -> nil activate(n__o) -> o activate(n__u) -> u activate(X) -> X e -> n__e i -> n__i isList(n____(V1,V2)) -> U21(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList(n__nil) -> tt isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,__(P,I))) -> U71(isQid(activate(I)),activate(I),activate(P)) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isPal(n__nil) -> tt isPal(V) -> U81(isPalListKind(activate(V)),activate(V)) isPalListKind(n____(V1,V2)) -> U91(isPalListKind(activate(V1)),activate(V2)) isPalListKind(n__a) -> tt isPalListKind(n__e) -> tt isPalListKind(n__i) -> tt isPalListKind(n__nil) -> tt isPalListKind(n__o) -> tt isPalListKind(n__u) -> tt isQid(n__a) -> tt isQid(n__e) -> tt isQid(n__i) -> tt isQid(n__o) -> tt isQid(n__u) -> tt nil -> n__nil o -> n__o u -> n__u ->->Cycle: ->->-> Pairs: U91#(tt,V2) -> ISPALLISTKIND(activate(V2)) ISPALLISTKIND(n____(V1,V2)) -> U91#(isPalListKind(activate(V1)),activate(V2)) ISPALLISTKIND(n____(V1,V2)) -> ISPALLISTKIND(activate(V1)) ->->-> Rules: U11(tt,V) -> U12(isPalListKind(activate(V)),activate(V)) U12(tt,V) -> U13(isNeList(activate(V))) U13(tt) -> tt U21(tt,V1,V2) -> U22(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22(tt,V1,V2) -> U23(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23(tt,V1,V2) -> U24(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24(tt,V1,V2) -> U25(isList(activate(V1)),activate(V2)) U25(tt,V2) -> U26(isList(activate(V2))) U26(tt) -> tt U31(tt,V) -> U32(isPalListKind(activate(V)),activate(V)) U32(tt,V) -> U33(isQid(activate(V))) U33(tt) -> tt U41(tt,V1,V2) -> U42(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42(tt,V1,V2) -> U43(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43(tt,V1,V2) -> U44(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44(tt,V1,V2) -> U45(isList(activate(V1)),activate(V2)) U45(tt,V2) -> U46(isNeList(activate(V2))) U46(tt) -> tt U51(tt,V1,V2) -> U52(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52(tt,V1,V2) -> U53(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53(tt,V1,V2) -> U54(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54(tt,V1,V2) -> U55(isNeList(activate(V1)),activate(V2)) U55(tt,V2) -> U56(isList(activate(V2))) U56(tt) -> tt U61(tt,V) -> U62(isPalListKind(activate(V)),activate(V)) U62(tt,V) -> U63(isQid(activate(V))) U63(tt) -> tt U71(tt,I,P) -> U72(isPalListKind(activate(I)),activate(P)) U72(tt,P) -> U73(isPal(activate(P)),activate(P)) U73(tt,P) -> U74(isPalListKind(activate(P))) U74(tt) -> tt U81(tt,V) -> U82(isPalListKind(activate(V)),activate(V)) U82(tt,V) -> U83(isNePal(activate(V))) U83(tt) -> tt U91(tt,V2) -> U92(isPalListKind(activate(V2))) U92(tt) -> tt __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil,X) -> X __(X,nil) -> X __(X1,X2) -> n____(X1,X2) a -> n__a activate(n____(X1,X2)) -> __(X1,X2) activate(n__a) -> a activate(n__e) -> e activate(n__i) -> i activate(n__nil) -> nil activate(n__o) -> o activate(n__u) -> u activate(X) -> X e -> n__e i -> n__i isList(n____(V1,V2)) -> U21(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList(n__nil) -> tt isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,__(P,I))) -> U71(isQid(activate(I)),activate(I),activate(P)) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isPal(n__nil) -> tt isPal(V) -> U81(isPalListKind(activate(V)),activate(V)) isPalListKind(n____(V1,V2)) -> U91(isPalListKind(activate(V1)),activate(V2)) isPalListKind(n__a) -> tt isPalListKind(n__e) -> tt isPalListKind(n__i) -> tt isPalListKind(n__nil) -> tt isPalListKind(n__o) -> tt isPalListKind(n__u) -> tt isQid(n__a) -> tt isQid(n__e) -> tt isQid(n__i) -> tt isQid(n__o) -> tt isQid(n__u) -> tt nil -> n__nil o -> n__o u -> n__u ->->Cycle: ->->-> Pairs: U71#(tt,I,P) -> U72#(isPalListKind(activate(I)),activate(P)) U72#(tt,P) -> ISPAL(activate(P)) U81#(tt,V) -> U82#(isPalListKind(activate(V)),activate(V)) U82#(tt,V) -> ISNEPAL(activate(V)) ISNEPAL(n____(I,__(P,I))) -> U71#(isQid(activate(I)),activate(I),activate(P)) ISPAL(V) -> U81#(isPalListKind(activate(V)),activate(V)) ->->-> Rules: U11(tt,V) -> U12(isPalListKind(activate(V)),activate(V)) U12(tt,V) -> U13(isNeList(activate(V))) U13(tt) -> tt U21(tt,V1,V2) -> U22(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22(tt,V1,V2) -> U23(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23(tt,V1,V2) -> U24(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24(tt,V1,V2) -> U25(isList(activate(V1)),activate(V2)) U25(tt,V2) -> U26(isList(activate(V2))) U26(tt) -> tt U31(tt,V) -> U32(isPalListKind(activate(V)),activate(V)) U32(tt,V) -> U33(isQid(activate(V))) U33(tt) -> tt U41(tt,V1,V2) -> U42(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42(tt,V1,V2) -> U43(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43(tt,V1,V2) -> U44(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44(tt,V1,V2) -> U45(isList(activate(V1)),activate(V2)) U45(tt,V2) -> U46(isNeList(activate(V2))) U46(tt) -> tt U51(tt,V1,V2) -> U52(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52(tt,V1,V2) -> U53(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53(tt,V1,V2) -> U54(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54(tt,V1,V2) -> U55(isNeList(activate(V1)),activate(V2)) U55(tt,V2) -> U56(isList(activate(V2))) U56(tt) -> tt U61(tt,V) -> U62(isPalListKind(activate(V)),activate(V)) U62(tt,V) -> U63(isQid(activate(V))) U63(tt) -> tt U71(tt,I,P) -> U72(isPalListKind(activate(I)),activate(P)) U72(tt,P) -> U73(isPal(activate(P)),activate(P)) U73(tt,P) -> U74(isPalListKind(activate(P))) U74(tt) -> tt U81(tt,V) -> U82(isPalListKind(activate(V)),activate(V)) U82(tt,V) -> U83(isNePal(activate(V))) U83(tt) -> tt U91(tt,V2) -> U92(isPalListKind(activate(V2))) U92(tt) -> tt __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil,X) -> X __(X,nil) -> X __(X1,X2) -> n____(X1,X2) a -> n__a activate(n____(X1,X2)) -> __(X1,X2) activate(n__a) -> a activate(n__e) -> e activate(n__i) -> i activate(n__nil) -> nil activate(n__o) -> o activate(n__u) -> u activate(X) -> X e -> n__e i -> n__i isList(n____(V1,V2)) -> U21(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList(n__nil) -> tt isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,__(P,I))) -> U71(isQid(activate(I)),activate(I),activate(P)) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isPal(n__nil) -> tt isPal(V) -> U81(isPalListKind(activate(V)),activate(V)) isPalListKind(n____(V1,V2)) -> U91(isPalListKind(activate(V1)),activate(V2)) isPalListKind(n__a) -> tt isPalListKind(n__e) -> tt isPalListKind(n__i) -> tt isPalListKind(n__nil) -> tt isPalListKind(n__o) -> tt isPalListKind(n__u) -> tt isQid(n__a) -> tt isQid(n__e) -> tt isQid(n__i) -> tt isQid(n__o) -> tt isQid(n__u) -> tt nil -> n__nil o -> n__o u -> n__u ->->Cycle: ->->-> Pairs: U11#(tt,V) -> U12#(isPalListKind(activate(V)),activate(V)) U12#(tt,V) -> ISNELIST(activate(V)) U21#(tt,V1,V2) -> U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22#(tt,V1,V2) -> U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23#(tt,V1,V2) -> U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24#(tt,V1,V2) -> U25#(isList(activate(V1)),activate(V2)) U24#(tt,V1,V2) -> ISLIST(activate(V1)) U25#(tt,V2) -> ISLIST(activate(V2)) U41#(tt,V1,V2) -> U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42#(tt,V1,V2) -> U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43#(tt,V1,V2) -> U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44#(tt,V1,V2) -> U45#(isList(activate(V1)),activate(V2)) U44#(tt,V1,V2) -> ISLIST(activate(V1)) U45#(tt,V2) -> ISNELIST(activate(V2)) U51#(tt,V1,V2) -> U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52#(tt,V1,V2) -> U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53#(tt,V1,V2) -> U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54#(tt,V1,V2) -> U55#(isNeList(activate(V1)),activate(V2)) U54#(tt,V1,V2) -> ISNELIST(activate(V1)) U55#(tt,V2) -> ISLIST(activate(V2)) ISLIST(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ISLIST(V) -> U11#(isPalListKind(activate(V)),activate(V)) ISNELIST(n____(V1,V2)) -> U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ISNELIST(n____(V1,V2)) -> U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ->->-> Rules: U11(tt,V) -> U12(isPalListKind(activate(V)),activate(V)) U12(tt,V) -> U13(isNeList(activate(V))) U13(tt) -> tt U21(tt,V1,V2) -> U22(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22(tt,V1,V2) -> U23(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23(tt,V1,V2) -> U24(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24(tt,V1,V2) -> U25(isList(activate(V1)),activate(V2)) U25(tt,V2) -> U26(isList(activate(V2))) U26(tt) -> tt U31(tt,V) -> U32(isPalListKind(activate(V)),activate(V)) U32(tt,V) -> U33(isQid(activate(V))) U33(tt) -> tt U41(tt,V1,V2) -> U42(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42(tt,V1,V2) -> U43(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43(tt,V1,V2) -> U44(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44(tt,V1,V2) -> U45(isList(activate(V1)),activate(V2)) U45(tt,V2) -> U46(isNeList(activate(V2))) U46(tt) -> tt U51(tt,V1,V2) -> U52(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52(tt,V1,V2) -> U53(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53(tt,V1,V2) -> U54(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54(tt,V1,V2) -> U55(isNeList(activate(V1)),activate(V2)) U55(tt,V2) -> U56(isList(activate(V2))) U56(tt) -> tt U61(tt,V) -> U62(isPalListKind(activate(V)),activate(V)) U62(tt,V) -> U63(isQid(activate(V))) U63(tt) -> tt U71(tt,I,P) -> U72(isPalListKind(activate(I)),activate(P)) U72(tt,P) -> U73(isPal(activate(P)),activate(P)) U73(tt,P) -> U74(isPalListKind(activate(P))) U74(tt) -> tt U81(tt,V) -> U82(isPalListKind(activate(V)),activate(V)) U82(tt,V) -> U83(isNePal(activate(V))) U83(tt) -> tt U91(tt,V2) -> U92(isPalListKind(activate(V2))) U92(tt) -> tt __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil,X) -> X __(X,nil) -> X __(X1,X2) -> n____(X1,X2) a -> n__a activate(n____(X1,X2)) -> __(X1,X2) activate(n__a) -> a activate(n__e) -> e activate(n__i) -> i activate(n__nil) -> nil activate(n__o) -> o activate(n__u) -> u activate(X) -> X e -> n__e i -> n__i isList(n____(V1,V2)) -> U21(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList(n__nil) -> tt isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,__(P,I))) -> U71(isQid(activate(I)),activate(I),activate(P)) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isPal(n__nil) -> tt isPal(V) -> U81(isPalListKind(activate(V)),activate(V)) isPalListKind(n____(V1,V2)) -> U91(isPalListKind(activate(V1)),activate(V2)) isPalListKind(n__a) -> tt isPalListKind(n__e) -> tt isPalListKind(n__i) -> tt isPalListKind(n__nil) -> tt isPalListKind(n__o) -> tt isPalListKind(n__u) -> tt isQid(n__a) -> tt isQid(n__e) -> tt isQid(n__i) -> tt isQid(n__o) -> tt isQid(n__u) -> tt nil -> n__nil o -> n__o u -> n__u The problem is decomposed in 4 subproblems. Problem 1.1: Subterm Processor: -> Pairs: __#(__(X,Y),Z) -> __#(X,__(Y,Z)) __#(__(X,Y),Z) -> __#(Y,Z) -> Rules: U11(tt,V) -> U12(isPalListKind(activate(V)),activate(V)) U12(tt,V) -> U13(isNeList(activate(V))) U13(tt) -> tt U21(tt,V1,V2) -> U22(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22(tt,V1,V2) -> U23(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23(tt,V1,V2) -> U24(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24(tt,V1,V2) -> U25(isList(activate(V1)),activate(V2)) U25(tt,V2) -> U26(isList(activate(V2))) U26(tt) -> tt U31(tt,V) -> U32(isPalListKind(activate(V)),activate(V)) U32(tt,V) -> U33(isQid(activate(V))) U33(tt) -> tt U41(tt,V1,V2) -> U42(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42(tt,V1,V2) -> U43(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43(tt,V1,V2) -> U44(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44(tt,V1,V2) -> U45(isList(activate(V1)),activate(V2)) U45(tt,V2) -> U46(isNeList(activate(V2))) U46(tt) -> tt U51(tt,V1,V2) -> U52(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52(tt,V1,V2) -> U53(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53(tt,V1,V2) -> U54(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54(tt,V1,V2) -> U55(isNeList(activate(V1)),activate(V2)) U55(tt,V2) -> U56(isList(activate(V2))) U56(tt) -> tt U61(tt,V) -> U62(isPalListKind(activate(V)),activate(V)) U62(tt,V) -> U63(isQid(activate(V))) U63(tt) -> tt U71(tt,I,P) -> U72(isPalListKind(activate(I)),activate(P)) U72(tt,P) -> U73(isPal(activate(P)),activate(P)) U73(tt,P) -> U74(isPalListKind(activate(P))) U74(tt) -> tt U81(tt,V) -> U82(isPalListKind(activate(V)),activate(V)) U82(tt,V) -> U83(isNePal(activate(V))) U83(tt) -> tt U91(tt,V2) -> U92(isPalListKind(activate(V2))) U92(tt) -> tt __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil,X) -> X __(X,nil) -> X __(X1,X2) -> n____(X1,X2) a -> n__a activate(n____(X1,X2)) -> __(X1,X2) activate(n__a) -> a activate(n__e) -> e activate(n__i) -> i activate(n__nil) -> nil activate(n__o) -> o activate(n__u) -> u activate(X) -> X e -> n__e i -> n__i isList(n____(V1,V2)) -> U21(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList(n__nil) -> tt isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,__(P,I))) -> U71(isQid(activate(I)),activate(I),activate(P)) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isPal(n__nil) -> tt isPal(V) -> U81(isPalListKind(activate(V)),activate(V)) isPalListKind(n____(V1,V2)) -> U91(isPalListKind(activate(V1)),activate(V2)) isPalListKind(n__a) -> tt isPalListKind(n__e) -> tt isPalListKind(n__i) -> tt isPalListKind(n__nil) -> tt isPalListKind(n__o) -> tt isPalListKind(n__u) -> tt isQid(n__a) -> tt isQid(n__e) -> tt isQid(n__i) -> tt isQid(n__o) -> tt isQid(n__u) -> tt nil -> n__nil o -> n__o u -> n__u ->Projection: pi(__#) = 1 Problem 1.1: SCC Processor: -> Pairs: Empty -> Rules: U11(tt,V) -> U12(isPalListKind(activate(V)),activate(V)) U12(tt,V) -> U13(isNeList(activate(V))) U13(tt) -> tt U21(tt,V1,V2) -> U22(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22(tt,V1,V2) -> U23(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23(tt,V1,V2) -> U24(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24(tt,V1,V2) -> U25(isList(activate(V1)),activate(V2)) U25(tt,V2) -> U26(isList(activate(V2))) U26(tt) -> tt U31(tt,V) -> U32(isPalListKind(activate(V)),activate(V)) U32(tt,V) -> U33(isQid(activate(V))) U33(tt) -> tt U41(tt,V1,V2) -> U42(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42(tt,V1,V2) -> U43(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43(tt,V1,V2) -> U44(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44(tt,V1,V2) -> U45(isList(activate(V1)),activate(V2)) U45(tt,V2) -> U46(isNeList(activate(V2))) U46(tt) -> tt U51(tt,V1,V2) -> U52(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52(tt,V1,V2) -> U53(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53(tt,V1,V2) -> U54(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54(tt,V1,V2) -> U55(isNeList(activate(V1)),activate(V2)) U55(tt,V2) -> U56(isList(activate(V2))) U56(tt) -> tt U61(tt,V) -> U62(isPalListKind(activate(V)),activate(V)) U62(tt,V) -> U63(isQid(activate(V))) U63(tt) -> tt U71(tt,I,P) -> U72(isPalListKind(activate(I)),activate(P)) U72(tt,P) -> U73(isPal(activate(P)),activate(P)) U73(tt,P) -> U74(isPalListKind(activate(P))) U74(tt) -> tt U81(tt,V) -> U82(isPalListKind(activate(V)),activate(V)) U82(tt,V) -> U83(isNePal(activate(V))) U83(tt) -> tt U91(tt,V2) -> U92(isPalListKind(activate(V2))) U92(tt) -> tt __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil,X) -> X __(X,nil) -> X __(X1,X2) -> n____(X1,X2) a -> n__a activate(n____(X1,X2)) -> __(X1,X2) activate(n__a) -> a activate(n__e) -> e activate(n__i) -> i activate(n__nil) -> nil activate(n__o) -> o activate(n__u) -> u activate(X) -> X e -> n__e i -> n__i isList(n____(V1,V2)) -> U21(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList(n__nil) -> tt isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,__(P,I))) -> U71(isQid(activate(I)),activate(I),activate(P)) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isPal(n__nil) -> tt isPal(V) -> U81(isPalListKind(activate(V)),activate(V)) isPalListKind(n____(V1,V2)) -> U91(isPalListKind(activate(V1)),activate(V2)) isPalListKind(n__a) -> tt isPalListKind(n__e) -> tt isPalListKind(n__i) -> tt isPalListKind(n__nil) -> tt isPalListKind(n__o) -> tt isPalListKind(n__u) -> tt isQid(n__a) -> tt isQid(n__e) -> tt isQid(n__i) -> tt isQid(n__o) -> tt isQid(n__u) -> tt nil -> n__nil o -> n__o u -> n__u ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.2: Reduction Pair Processor: -> Pairs: U91#(tt,V2) -> ISPALLISTKIND(activate(V2)) ISPALLISTKIND(n____(V1,V2)) -> U91#(isPalListKind(activate(V1)),activate(V2)) ISPALLISTKIND(n____(V1,V2)) -> ISPALLISTKIND(activate(V1)) -> Rules: U11(tt,V) -> U12(isPalListKind(activate(V)),activate(V)) U12(tt,V) -> U13(isNeList(activate(V))) U13(tt) -> tt U21(tt,V1,V2) -> U22(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22(tt,V1,V2) -> U23(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23(tt,V1,V2) -> U24(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24(tt,V1,V2) -> U25(isList(activate(V1)),activate(V2)) U25(tt,V2) -> U26(isList(activate(V2))) U26(tt) -> tt U31(tt,V) -> U32(isPalListKind(activate(V)),activate(V)) U32(tt,V) -> U33(isQid(activate(V))) U33(tt) -> tt U41(tt,V1,V2) -> U42(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42(tt,V1,V2) -> U43(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43(tt,V1,V2) -> U44(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44(tt,V1,V2) -> U45(isList(activate(V1)),activate(V2)) U45(tt,V2) -> U46(isNeList(activate(V2))) U46(tt) -> tt U51(tt,V1,V2) -> U52(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52(tt,V1,V2) -> U53(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53(tt,V1,V2) -> U54(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54(tt,V1,V2) -> U55(isNeList(activate(V1)),activate(V2)) U55(tt,V2) -> U56(isList(activate(V2))) U56(tt) -> tt U61(tt,V) -> U62(isPalListKind(activate(V)),activate(V)) U62(tt,V) -> U63(isQid(activate(V))) U63(tt) -> tt U71(tt,I,P) -> U72(isPalListKind(activate(I)),activate(P)) U72(tt,P) -> U73(isPal(activate(P)),activate(P)) U73(tt,P) -> U74(isPalListKind(activate(P))) U74(tt) -> tt U81(tt,V) -> U82(isPalListKind(activate(V)),activate(V)) U82(tt,V) -> U83(isNePal(activate(V))) U83(tt) -> tt U91(tt,V2) -> U92(isPalListKind(activate(V2))) U92(tt) -> tt __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil,X) -> X __(X,nil) -> X __(X1,X2) -> n____(X1,X2) a -> n__a activate(n____(X1,X2)) -> __(X1,X2) activate(n__a) -> a activate(n__e) -> e activate(n__i) -> i activate(n__nil) -> nil activate(n__o) -> o activate(n__u) -> u activate(X) -> X e -> n__e i -> n__i isList(n____(V1,V2)) -> U21(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList(n__nil) -> tt isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,__(P,I))) -> U71(isQid(activate(I)),activate(I),activate(P)) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isPal(n__nil) -> tt isPal(V) -> U81(isPalListKind(activate(V)),activate(V)) isPalListKind(n____(V1,V2)) -> U91(isPalListKind(activate(V1)),activate(V2)) isPalListKind(n__a) -> tt isPalListKind(n__e) -> tt isPalListKind(n__i) -> tt isPalListKind(n__nil) -> tt isPalListKind(n__o) -> tt isPalListKind(n__u) -> tt isQid(n__a) -> tt isQid(n__e) -> tt isQid(n__i) -> tt isQid(n__o) -> tt isQid(n__u) -> tt nil -> n__nil o -> n__o u -> n__u -> Usable rules: U91(tt,V2) -> U92(isPalListKind(activate(V2))) U92(tt) -> tt __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil,X) -> X __(X,nil) -> X __(X1,X2) -> n____(X1,X2) a -> n__a activate(n____(X1,X2)) -> __(X1,X2) activate(n__a) -> a activate(n__e) -> e activate(n__i) -> i activate(n__nil) -> nil activate(n__o) -> o activate(n__u) -> u activate(X) -> X e -> n__e i -> n__i isPalListKind(n____(V1,V2)) -> U91(isPalListKind(activate(V1)),activate(V2)) isPalListKind(n__a) -> tt isPalListKind(n__e) -> tt isPalListKind(n__i) -> tt isPalListKind(n__nil) -> tt isPalListKind(n__o) -> tt isPalListKind(n__u) -> tt nil -> n__nil o -> n__o u -> n__u ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 2 ->Bound: 1 ->Interpretation: [U91](X1,X2) = [1 0;1 1].X1 + [1 0;0 0].X2 + [1;1] [U92](X) = [1 0;0 0].X + [1;1] [__](X1,X2) = [1 1;1 1].X1 + [1 0;0 1].X2 + [1;1] [a] = [1;1] [activate](X) = [1 0;0 1].X + [0;1] [e] = [1;1] [i] = [1;1] [isPalListKind](X) = [1 0;1 1].X [nil] = [1;1] [o] = [1;1] [u] = [1;0] [n____](X1,X2) = [1 1;1 1].X1 + [1 0;0 1].X2 + [1;1] [n__a] = [1;0] [n__e] = [1;1] [n__i] = [1;1] [n__nil] = [1;1] [n__o] = [1;1] [n__u] = [1;0] [tt] = [1;1] [U91#](X1,X2) = [1 1;0 1].X1 + [1 1;1 1].X2 + [1;1] [ISPALLISTKIND](X) = [1 1;1 1].X + [1;1] Problem 1.2: SCC Processor: -> Pairs: ISPALLISTKIND(n____(V1,V2)) -> U91#(isPalListKind(activate(V1)),activate(V2)) ISPALLISTKIND(n____(V1,V2)) -> ISPALLISTKIND(activate(V1)) -> Rules: U11(tt,V) -> U12(isPalListKind(activate(V)),activate(V)) U12(tt,V) -> U13(isNeList(activate(V))) U13(tt) -> tt U21(tt,V1,V2) -> U22(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22(tt,V1,V2) -> U23(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23(tt,V1,V2) -> U24(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24(tt,V1,V2) -> U25(isList(activate(V1)),activate(V2)) U25(tt,V2) -> U26(isList(activate(V2))) U26(tt) -> tt U31(tt,V) -> U32(isPalListKind(activate(V)),activate(V)) U32(tt,V) -> U33(isQid(activate(V))) U33(tt) -> tt U41(tt,V1,V2) -> U42(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42(tt,V1,V2) -> U43(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43(tt,V1,V2) -> U44(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44(tt,V1,V2) -> U45(isList(activate(V1)),activate(V2)) U45(tt,V2) -> U46(isNeList(activate(V2))) U46(tt) -> tt U51(tt,V1,V2) -> U52(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52(tt,V1,V2) -> U53(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53(tt,V1,V2) -> U54(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54(tt,V1,V2) -> U55(isNeList(activate(V1)),activate(V2)) U55(tt,V2) -> U56(isList(activate(V2))) U56(tt) -> tt U61(tt,V) -> U62(isPalListKind(activate(V)),activate(V)) U62(tt,V) -> U63(isQid(activate(V))) U63(tt) -> tt U71(tt,I,P) -> U72(isPalListKind(activate(I)),activate(P)) U72(tt,P) -> U73(isPal(activate(P)),activate(P)) U73(tt,P) -> U74(isPalListKind(activate(P))) U74(tt) -> tt U81(tt,V) -> U82(isPalListKind(activate(V)),activate(V)) U82(tt,V) -> U83(isNePal(activate(V))) U83(tt) -> tt U91(tt,V2) -> U92(isPalListKind(activate(V2))) U92(tt) -> tt __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil,X) -> X __(X,nil) -> X __(X1,X2) -> n____(X1,X2) a -> n__a activate(n____(X1,X2)) -> __(X1,X2) activate(n__a) -> a activate(n__e) -> e activate(n__i) -> i activate(n__nil) -> nil activate(n__o) -> o activate(n__u) -> u activate(X) -> X e -> n__e i -> n__i isList(n____(V1,V2)) -> U21(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList(n__nil) -> tt isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,__(P,I))) -> U71(isQid(activate(I)),activate(I),activate(P)) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isPal(n__nil) -> tt isPal(V) -> U81(isPalListKind(activate(V)),activate(V)) isPalListKind(n____(V1,V2)) -> U91(isPalListKind(activate(V1)),activate(V2)) isPalListKind(n__a) -> tt isPalListKind(n__e) -> tt isPalListKind(n__i) -> tt isPalListKind(n__nil) -> tt isPalListKind(n__o) -> tt isPalListKind(n__u) -> tt isQid(n__a) -> tt isQid(n__e) -> tt isQid(n__i) -> tt isQid(n__o) -> tt isQid(n__u) -> tt nil -> n__nil o -> n__o u -> n__u ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ISPALLISTKIND(n____(V1,V2)) -> ISPALLISTKIND(activate(V1)) ->->-> Rules: U11(tt,V) -> U12(isPalListKind(activate(V)),activate(V)) U12(tt,V) -> U13(isNeList(activate(V))) U13(tt) -> tt U21(tt,V1,V2) -> U22(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22(tt,V1,V2) -> U23(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23(tt,V1,V2) -> U24(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24(tt,V1,V2) -> U25(isList(activate(V1)),activate(V2)) U25(tt,V2) -> U26(isList(activate(V2))) U26(tt) -> tt U31(tt,V) -> U32(isPalListKind(activate(V)),activate(V)) U32(tt,V) -> U33(isQid(activate(V))) U33(tt) -> tt U41(tt,V1,V2) -> U42(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42(tt,V1,V2) -> U43(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43(tt,V1,V2) -> U44(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44(tt,V1,V2) -> U45(isList(activate(V1)),activate(V2)) U45(tt,V2) -> U46(isNeList(activate(V2))) U46(tt) -> tt U51(tt,V1,V2) -> U52(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52(tt,V1,V2) -> U53(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53(tt,V1,V2) -> U54(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54(tt,V1,V2) -> U55(isNeList(activate(V1)),activate(V2)) U55(tt,V2) -> U56(isList(activate(V2))) U56(tt) -> tt U61(tt,V) -> U62(isPalListKind(activate(V)),activate(V)) U62(tt,V) -> U63(isQid(activate(V))) U63(tt) -> tt U71(tt,I,P) -> U72(isPalListKind(activate(I)),activate(P)) U72(tt,P) -> U73(isPal(activate(P)),activate(P)) U73(tt,P) -> U74(isPalListKind(activate(P))) U74(tt) -> tt U81(tt,V) -> U82(isPalListKind(activate(V)),activate(V)) U82(tt,V) -> U83(isNePal(activate(V))) U83(tt) -> tt U91(tt,V2) -> U92(isPalListKind(activate(V2))) U92(tt) -> tt __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil,X) -> X __(X,nil) -> X __(X1,X2) -> n____(X1,X2) a -> n__a activate(n____(X1,X2)) -> __(X1,X2) activate(n__a) -> a activate(n__e) -> e activate(n__i) -> i activate(n__nil) -> nil activate(n__o) -> o activate(n__u) -> u activate(X) -> X e -> n__e i -> n__i isList(n____(V1,V2)) -> U21(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList(n__nil) -> tt isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,__(P,I))) -> U71(isQid(activate(I)),activate(I),activate(P)) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isPal(n__nil) -> tt isPal(V) -> U81(isPalListKind(activate(V)),activate(V)) isPalListKind(n____(V1,V2)) -> U91(isPalListKind(activate(V1)),activate(V2)) isPalListKind(n__a) -> tt isPalListKind(n__e) -> tt isPalListKind(n__i) -> tt isPalListKind(n__nil) -> tt isPalListKind(n__o) -> tt isPalListKind(n__u) -> tt isQid(n__a) -> tt isQid(n__e) -> tt isQid(n__i) -> tt isQid(n__o) -> tt isQid(n__u) -> tt nil -> n__nil o -> n__o u -> n__u Problem 1.2: Reduction Pair Processor: -> Pairs: ISPALLISTKIND(n____(V1,V2)) -> ISPALLISTKIND(activate(V1)) -> Rules: U11(tt,V) -> U12(isPalListKind(activate(V)),activate(V)) U12(tt,V) -> U13(isNeList(activate(V))) U13(tt) -> tt U21(tt,V1,V2) -> U22(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22(tt,V1,V2) -> U23(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23(tt,V1,V2) -> U24(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24(tt,V1,V2) -> U25(isList(activate(V1)),activate(V2)) U25(tt,V2) -> U26(isList(activate(V2))) U26(tt) -> tt U31(tt,V) -> U32(isPalListKind(activate(V)),activate(V)) U32(tt,V) -> U33(isQid(activate(V))) U33(tt) -> tt U41(tt,V1,V2) -> U42(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42(tt,V1,V2) -> U43(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43(tt,V1,V2) -> U44(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44(tt,V1,V2) -> U45(isList(activate(V1)),activate(V2)) U45(tt,V2) -> U46(isNeList(activate(V2))) U46(tt) -> tt U51(tt,V1,V2) -> U52(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52(tt,V1,V2) -> U53(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53(tt,V1,V2) -> U54(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54(tt,V1,V2) -> U55(isNeList(activate(V1)),activate(V2)) U55(tt,V2) -> U56(isList(activate(V2))) U56(tt) -> tt U61(tt,V) -> U62(isPalListKind(activate(V)),activate(V)) U62(tt,V) -> U63(isQid(activate(V))) U63(tt) -> tt U71(tt,I,P) -> U72(isPalListKind(activate(I)),activate(P)) U72(tt,P) -> U73(isPal(activate(P)),activate(P)) U73(tt,P) -> U74(isPalListKind(activate(P))) U74(tt) -> tt U81(tt,V) -> U82(isPalListKind(activate(V)),activate(V)) U82(tt,V) -> U83(isNePal(activate(V))) U83(tt) -> tt U91(tt,V2) -> U92(isPalListKind(activate(V2))) U92(tt) -> tt __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil,X) -> X __(X,nil) -> X __(X1,X2) -> n____(X1,X2) a -> n__a activate(n____(X1,X2)) -> __(X1,X2) activate(n__a) -> a activate(n__e) -> e activate(n__i) -> i activate(n__nil) -> nil activate(n__o) -> o activate(n__u) -> u activate(X) -> X e -> n__e i -> n__i isList(n____(V1,V2)) -> U21(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList(n__nil) -> tt isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,__(P,I))) -> U71(isQid(activate(I)),activate(I),activate(P)) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isPal(n__nil) -> tt isPal(V) -> U81(isPalListKind(activate(V)),activate(V)) isPalListKind(n____(V1,V2)) -> U91(isPalListKind(activate(V1)),activate(V2)) isPalListKind(n__a) -> tt isPalListKind(n__e) -> tt isPalListKind(n__i) -> tt isPalListKind(n__nil) -> tt isPalListKind(n__o) -> tt isPalListKind(n__u) -> tt isQid(n__a) -> tt isQid(n__e) -> tt isQid(n__i) -> tt isQid(n__o) -> tt isQid(n__u) -> tt nil -> n__nil o -> n__o u -> n__u -> Usable rules: __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil,X) -> X __(X,nil) -> X __(X1,X2) -> n____(X1,X2) a -> n__a activate(n____(X1,X2)) -> __(X1,X2) activate(n__a) -> a activate(n__e) -> e activate(n__i) -> i activate(n__nil) -> nil activate(n__o) -> o activate(n__u) -> u activate(X) -> X e -> n__e i -> n__i nil -> n__nil o -> n__o u -> n__u ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [__](X1,X2) = 2.X1 + X2 + 2 [a] = 1 [activate](X) = 2.X + 1 [e] = 1 [i] = 0 [nil] = 1 [o] = 1 [u] = 1 [n____](X1,X2) = 2.X1 + X2 + 2 [n__a] = 0 [n__e] = 0 [n__i] = 0 [n__nil] = 0 [n__o] = 0 [n__u] = 0 [ISPALLISTKIND](X) = 2.X Problem 1.2: SCC Processor: -> Pairs: Empty -> Rules: U11(tt,V) -> U12(isPalListKind(activate(V)),activate(V)) U12(tt,V) -> U13(isNeList(activate(V))) U13(tt) -> tt U21(tt,V1,V2) -> U22(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22(tt,V1,V2) -> U23(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23(tt,V1,V2) -> U24(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24(tt,V1,V2) -> U25(isList(activate(V1)),activate(V2)) U25(tt,V2) -> U26(isList(activate(V2))) U26(tt) -> tt U31(tt,V) -> U32(isPalListKind(activate(V)),activate(V)) U32(tt,V) -> U33(isQid(activate(V))) U33(tt) -> tt U41(tt,V1,V2) -> U42(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42(tt,V1,V2) -> U43(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43(tt,V1,V2) -> U44(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44(tt,V1,V2) -> U45(isList(activate(V1)),activate(V2)) U45(tt,V2) -> U46(isNeList(activate(V2))) U46(tt) -> tt U51(tt,V1,V2) -> U52(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52(tt,V1,V2) -> U53(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53(tt,V1,V2) -> U54(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54(tt,V1,V2) -> U55(isNeList(activate(V1)),activate(V2)) U55(tt,V2) -> U56(isList(activate(V2))) U56(tt) -> tt U61(tt,V) -> U62(isPalListKind(activate(V)),activate(V)) U62(tt,V) -> U63(isQid(activate(V))) U63(tt) -> tt U71(tt,I,P) -> U72(isPalListKind(activate(I)),activate(P)) U72(tt,P) -> U73(isPal(activate(P)),activate(P)) U73(tt,P) -> U74(isPalListKind(activate(P))) U74(tt) -> tt U81(tt,V) -> U82(isPalListKind(activate(V)),activate(V)) U82(tt,V) -> U83(isNePal(activate(V))) U83(tt) -> tt U91(tt,V2) -> U92(isPalListKind(activate(V2))) U92(tt) -> tt __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil,X) -> X __(X,nil) -> X __(X1,X2) -> n____(X1,X2) a -> n__a activate(n____(X1,X2)) -> __(X1,X2) activate(n__a) -> a activate(n__e) -> e activate(n__i) -> i activate(n__nil) -> nil activate(n__o) -> o activate(n__u) -> u activate(X) -> X e -> n__e i -> n__i isList(n____(V1,V2)) -> U21(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList(n__nil) -> tt isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,__(P,I))) -> U71(isQid(activate(I)),activate(I),activate(P)) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isPal(n__nil) -> tt isPal(V) -> U81(isPalListKind(activate(V)),activate(V)) isPalListKind(n____(V1,V2)) -> U91(isPalListKind(activate(V1)),activate(V2)) isPalListKind(n__a) -> tt isPalListKind(n__e) -> tt isPalListKind(n__i) -> tt isPalListKind(n__nil) -> tt isPalListKind(n__o) -> tt isPalListKind(n__u) -> tt isQid(n__a) -> tt isQid(n__e) -> tt isQid(n__i) -> tt isQid(n__o) -> tt isQid(n__u) -> tt nil -> n__nil o -> n__o u -> n__u ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.3: Reduction Pair Processor: -> Pairs: U71#(tt,I,P) -> U72#(isPalListKind(activate(I)),activate(P)) U72#(tt,P) -> ISPAL(activate(P)) U81#(tt,V) -> U82#(isPalListKind(activate(V)),activate(V)) U82#(tt,V) -> ISNEPAL(activate(V)) ISNEPAL(n____(I,__(P,I))) -> U71#(isQid(activate(I)),activate(I),activate(P)) ISPAL(V) -> U81#(isPalListKind(activate(V)),activate(V)) -> Rules: U11(tt,V) -> U12(isPalListKind(activate(V)),activate(V)) U12(tt,V) -> U13(isNeList(activate(V))) U13(tt) -> tt U21(tt,V1,V2) -> U22(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22(tt,V1,V2) -> U23(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23(tt,V1,V2) -> U24(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24(tt,V1,V2) -> U25(isList(activate(V1)),activate(V2)) U25(tt,V2) -> U26(isList(activate(V2))) U26(tt) -> tt U31(tt,V) -> U32(isPalListKind(activate(V)),activate(V)) U32(tt,V) -> U33(isQid(activate(V))) U33(tt) -> tt U41(tt,V1,V2) -> U42(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42(tt,V1,V2) -> U43(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43(tt,V1,V2) -> U44(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44(tt,V1,V2) -> U45(isList(activate(V1)),activate(V2)) U45(tt,V2) -> U46(isNeList(activate(V2))) U46(tt) -> tt U51(tt,V1,V2) -> U52(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52(tt,V1,V2) -> U53(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53(tt,V1,V2) -> U54(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54(tt,V1,V2) -> U55(isNeList(activate(V1)),activate(V2)) U55(tt,V2) -> U56(isList(activate(V2))) U56(tt) -> tt U61(tt,V) -> U62(isPalListKind(activate(V)),activate(V)) U62(tt,V) -> U63(isQid(activate(V))) U63(tt) -> tt U71(tt,I,P) -> U72(isPalListKind(activate(I)),activate(P)) U72(tt,P) -> U73(isPal(activate(P)),activate(P)) U73(tt,P) -> U74(isPalListKind(activate(P))) U74(tt) -> tt U81(tt,V) -> U82(isPalListKind(activate(V)),activate(V)) U82(tt,V) -> U83(isNePal(activate(V))) U83(tt) -> tt U91(tt,V2) -> U92(isPalListKind(activate(V2))) U92(tt) -> tt __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil,X) -> X __(X,nil) -> X __(X1,X2) -> n____(X1,X2) a -> n__a activate(n____(X1,X2)) -> __(X1,X2) activate(n__a) -> a activate(n__e) -> e activate(n__i) -> i activate(n__nil) -> nil activate(n__o) -> o activate(n__u) -> u activate(X) -> X e -> n__e i -> n__i isList(n____(V1,V2)) -> U21(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList(n__nil) -> tt isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,__(P,I))) -> U71(isQid(activate(I)),activate(I),activate(P)) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isPal(n__nil) -> tt isPal(V) -> U81(isPalListKind(activate(V)),activate(V)) isPalListKind(n____(V1,V2)) -> U91(isPalListKind(activate(V1)),activate(V2)) isPalListKind(n__a) -> tt isPalListKind(n__e) -> tt isPalListKind(n__i) -> tt isPalListKind(n__nil) -> tt isPalListKind(n__o) -> tt isPalListKind(n__u) -> tt isQid(n__a) -> tt isQid(n__e) -> tt isQid(n__i) -> tt isQid(n__o) -> tt isQid(n__u) -> tt nil -> n__nil o -> n__o u -> n__u -> Usable rules: U91(tt,V2) -> U92(isPalListKind(activate(V2))) U92(tt) -> tt __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil,X) -> X __(X,nil) -> X __(X1,X2) -> n____(X1,X2) a -> n__a activate(n____(X1,X2)) -> __(X1,X2) activate(n__a) -> a activate(n__e) -> e activate(n__i) -> i activate(n__nil) -> nil activate(n__o) -> o activate(n__u) -> u activate(X) -> X e -> n__e i -> n__i isPalListKind(n____(V1,V2)) -> U91(isPalListKind(activate(V1)),activate(V2)) isPalListKind(n__a) -> tt isPalListKind(n__e) -> tt isPalListKind(n__i) -> tt isPalListKind(n__nil) -> tt isPalListKind(n__o) -> tt isPalListKind(n__u) -> tt isQid(n__a) -> tt isQid(n__e) -> tt isQid(n__i) -> tt isQid(n__o) -> tt isQid(n__u) -> tt nil -> n__nil o -> n__o u -> n__u ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U91](X1,X2) = 2.X1 + 1 [U92](X) = 2 [__](X1,X2) = 2.X1 + X2 + 2 [a] = 2 [activate](X) = X [e] = 1 [i] = 1 [isPalListKind](X) = X + 1 [isQid](X) = X + 2 [nil] = 1 [o] = 2 [u] = 2 [n____](X1,X2) = 2.X1 + X2 + 2 [n__a] = 2 [n__e] = 1 [n__i] = 1 [n__nil] = 1 [n__o] = 2 [n__u] = 2 [tt] = 2 [U71#](X1,X2,X3) = 2.X1 + X2 + 2.X3 + 1 [U72#](X1,X2) = 2.X2 + 2 [U81#](X1,X2) = X1 + X2 + 1 [U82#](X1,X2) = X2 + 1 [ISNEPAL](X) = X + 1 [ISPAL](X) = 2.X + 2 Problem 1.3: SCC Processor: -> Pairs: U72#(tt,P) -> ISPAL(activate(P)) U81#(tt,V) -> U82#(isPalListKind(activate(V)),activate(V)) U82#(tt,V) -> ISNEPAL(activate(V)) ISNEPAL(n____(I,__(P,I))) -> U71#(isQid(activate(I)),activate(I),activate(P)) ISPAL(V) -> U81#(isPalListKind(activate(V)),activate(V)) -> Rules: U11(tt,V) -> U12(isPalListKind(activate(V)),activate(V)) U12(tt,V) -> U13(isNeList(activate(V))) U13(tt) -> tt U21(tt,V1,V2) -> U22(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22(tt,V1,V2) -> U23(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23(tt,V1,V2) -> U24(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24(tt,V1,V2) -> U25(isList(activate(V1)),activate(V2)) U25(tt,V2) -> U26(isList(activate(V2))) U26(tt) -> tt U31(tt,V) -> U32(isPalListKind(activate(V)),activate(V)) U32(tt,V) -> U33(isQid(activate(V))) U33(tt) -> tt U41(tt,V1,V2) -> U42(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42(tt,V1,V2) -> U43(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43(tt,V1,V2) -> U44(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44(tt,V1,V2) -> U45(isList(activate(V1)),activate(V2)) U45(tt,V2) -> U46(isNeList(activate(V2))) U46(tt) -> tt U51(tt,V1,V2) -> U52(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52(tt,V1,V2) -> U53(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53(tt,V1,V2) -> U54(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54(tt,V1,V2) -> U55(isNeList(activate(V1)),activate(V2)) U55(tt,V2) -> U56(isList(activate(V2))) U56(tt) -> tt U61(tt,V) -> U62(isPalListKind(activate(V)),activate(V)) U62(tt,V) -> U63(isQid(activate(V))) U63(tt) -> tt U71(tt,I,P) -> U72(isPalListKind(activate(I)),activate(P)) U72(tt,P) -> U73(isPal(activate(P)),activate(P)) U73(tt,P) -> U74(isPalListKind(activate(P))) U74(tt) -> tt U81(tt,V) -> U82(isPalListKind(activate(V)),activate(V)) U82(tt,V) -> U83(isNePal(activate(V))) U83(tt) -> tt U91(tt,V2) -> U92(isPalListKind(activate(V2))) U92(tt) -> tt __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil,X) -> X __(X,nil) -> X __(X1,X2) -> n____(X1,X2) a -> n__a activate(n____(X1,X2)) -> __(X1,X2) activate(n__a) -> a activate(n__e) -> e activate(n__i) -> i activate(n__nil) -> nil activate(n__o) -> o activate(n__u) -> u activate(X) -> X e -> n__e i -> n__i isList(n____(V1,V2)) -> U21(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList(n__nil) -> tt isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,__(P,I))) -> U71(isQid(activate(I)),activate(I),activate(P)) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isPal(n__nil) -> tt isPal(V) -> U81(isPalListKind(activate(V)),activate(V)) isPalListKind(n____(V1,V2)) -> U91(isPalListKind(activate(V1)),activate(V2)) isPalListKind(n__a) -> tt isPalListKind(n__e) -> tt isPalListKind(n__i) -> tt isPalListKind(n__nil) -> tt isPalListKind(n__o) -> tt isPalListKind(n__u) -> tt isQid(n__a) -> tt isQid(n__e) -> tt isQid(n__i) -> tt isQid(n__o) -> tt isQid(n__u) -> tt nil -> n__nil o -> n__o u -> n__u ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.4: Reduction Pair Processor: -> Pairs: U11#(tt,V) -> U12#(isPalListKind(activate(V)),activate(V)) U12#(tt,V) -> ISNELIST(activate(V)) U21#(tt,V1,V2) -> U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22#(tt,V1,V2) -> U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23#(tt,V1,V2) -> U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24#(tt,V1,V2) -> U25#(isList(activate(V1)),activate(V2)) U24#(tt,V1,V2) -> ISLIST(activate(V1)) U25#(tt,V2) -> ISLIST(activate(V2)) U41#(tt,V1,V2) -> U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42#(tt,V1,V2) -> U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43#(tt,V1,V2) -> U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44#(tt,V1,V2) -> U45#(isList(activate(V1)),activate(V2)) U44#(tt,V1,V2) -> ISLIST(activate(V1)) U45#(tt,V2) -> ISNELIST(activate(V2)) U51#(tt,V1,V2) -> U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52#(tt,V1,V2) -> U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53#(tt,V1,V2) -> U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54#(tt,V1,V2) -> U55#(isNeList(activate(V1)),activate(V2)) U54#(tt,V1,V2) -> ISNELIST(activate(V1)) U55#(tt,V2) -> ISLIST(activate(V2)) ISLIST(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ISLIST(V) -> U11#(isPalListKind(activate(V)),activate(V)) ISNELIST(n____(V1,V2)) -> U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ISNELIST(n____(V1,V2)) -> U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)) -> Rules: U11(tt,V) -> U12(isPalListKind(activate(V)),activate(V)) U12(tt,V) -> U13(isNeList(activate(V))) U13(tt) -> tt U21(tt,V1,V2) -> U22(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22(tt,V1,V2) -> U23(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23(tt,V1,V2) -> U24(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24(tt,V1,V2) -> U25(isList(activate(V1)),activate(V2)) U25(tt,V2) -> U26(isList(activate(V2))) U26(tt) -> tt U31(tt,V) -> U32(isPalListKind(activate(V)),activate(V)) U32(tt,V) -> U33(isQid(activate(V))) U33(tt) -> tt U41(tt,V1,V2) -> U42(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42(tt,V1,V2) -> U43(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43(tt,V1,V2) -> U44(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44(tt,V1,V2) -> U45(isList(activate(V1)),activate(V2)) U45(tt,V2) -> U46(isNeList(activate(V2))) U46(tt) -> tt U51(tt,V1,V2) -> U52(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52(tt,V1,V2) -> U53(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53(tt,V1,V2) -> U54(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54(tt,V1,V2) -> U55(isNeList(activate(V1)),activate(V2)) U55(tt,V2) -> U56(isList(activate(V2))) U56(tt) -> tt U61(tt,V) -> U62(isPalListKind(activate(V)),activate(V)) U62(tt,V) -> U63(isQid(activate(V))) U63(tt) -> tt U71(tt,I,P) -> U72(isPalListKind(activate(I)),activate(P)) U72(tt,P) -> U73(isPal(activate(P)),activate(P)) U73(tt,P) -> U74(isPalListKind(activate(P))) U74(tt) -> tt U81(tt,V) -> U82(isPalListKind(activate(V)),activate(V)) U82(tt,V) -> U83(isNePal(activate(V))) U83(tt) -> tt U91(tt,V2) -> U92(isPalListKind(activate(V2))) U92(tt) -> tt __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil,X) -> X __(X,nil) -> X __(X1,X2) -> n____(X1,X2) a -> n__a activate(n____(X1,X2)) -> __(X1,X2) activate(n__a) -> a activate(n__e) -> e activate(n__i) -> i activate(n__nil) -> nil activate(n__o) -> o activate(n__u) -> u activate(X) -> X e -> n__e i -> n__i isList(n____(V1,V2)) -> U21(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList(n__nil) -> tt isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,__(P,I))) -> U71(isQid(activate(I)),activate(I),activate(P)) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isPal(n__nil) -> tt isPal(V) -> U81(isPalListKind(activate(V)),activate(V)) isPalListKind(n____(V1,V2)) -> U91(isPalListKind(activate(V1)),activate(V2)) isPalListKind(n__a) -> tt isPalListKind(n__e) -> tt isPalListKind(n__i) -> tt isPalListKind(n__nil) -> tt isPalListKind(n__o) -> tt isPalListKind(n__u) -> tt isQid(n__a) -> tt isQid(n__e) -> tt isQid(n__i) -> tt isQid(n__o) -> tt isQid(n__u) -> tt nil -> n__nil o -> n__o u -> n__u -> Usable rules: U11(tt,V) -> U12(isPalListKind(activate(V)),activate(V)) U12(tt,V) -> U13(isNeList(activate(V))) U13(tt) -> tt U21(tt,V1,V2) -> U22(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22(tt,V1,V2) -> U23(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23(tt,V1,V2) -> U24(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24(tt,V1,V2) -> U25(isList(activate(V1)),activate(V2)) U25(tt,V2) -> U26(isList(activate(V2))) U26(tt) -> tt U31(tt,V) -> U32(isPalListKind(activate(V)),activate(V)) U32(tt,V) -> U33(isQid(activate(V))) U33(tt) -> tt U41(tt,V1,V2) -> U42(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42(tt,V1,V2) -> U43(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43(tt,V1,V2) -> U44(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44(tt,V1,V2) -> U45(isList(activate(V1)),activate(V2)) U45(tt,V2) -> U46(isNeList(activate(V2))) U46(tt) -> tt U51(tt,V1,V2) -> U52(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52(tt,V1,V2) -> U53(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53(tt,V1,V2) -> U54(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54(tt,V1,V2) -> U55(isNeList(activate(V1)),activate(V2)) U55(tt,V2) -> U56(isList(activate(V2))) U56(tt) -> tt U91(tt,V2) -> U92(isPalListKind(activate(V2))) U92(tt) -> tt __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil,X) -> X __(X,nil) -> X __(X1,X2) -> n____(X1,X2) a -> n__a activate(n____(X1,X2)) -> __(X1,X2) activate(n__a) -> a activate(n__e) -> e activate(n__i) -> i activate(n__nil) -> nil activate(n__o) -> o activate(n__u) -> u activate(X) -> X e -> n__e i -> n__i isList(n____(V1,V2)) -> U21(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList(n__nil) -> tt isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isPalListKind(n____(V1,V2)) -> U91(isPalListKind(activate(V1)),activate(V2)) isPalListKind(n__a) -> tt isPalListKind(n__e) -> tt isPalListKind(n__i) -> tt isPalListKind(n__nil) -> tt isPalListKind(n__o) -> tt isPalListKind(n__u) -> tt isQid(n__a) -> tt isQid(n__e) -> tt isQid(n__i) -> tt isQid(n__o) -> tt isQid(n__u) -> tt nil -> n__nil o -> n__o u -> n__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) = 2 [U23](X1,X2,X3) = 2 [U24](X1,X2,X3) = 2 [U25](X1,X2) = 2 [U26](X) = 2 [U31](X1,X2) = 2.X2 + 2 [U32](X1,X2) = 2.X2 + 2 [U33](X) = X + 2 [U41](X1,X2,X3) = 2.X1 + 2.X3 + 2 [U42](X1,X2,X3) = 2.X3 + 2 [U43](X1,X2,X3) = 2.X3 + 2 [U44](X1,X2,X3) = X1 + 2 [U45](X1,X2) = 2 [U46](X) = 2 [U51](X1,X2,X3) = X1 + 2.X2 + 2.X3 [U52](X1,X2,X3) = 2.X2 + 2.X3 + 2 [U53](X1,X2,X3) = 2.X2 + 2.X3 + 2 [U54](X1,X2,X3) = 2.X2 + 2.X3 + 2 [U55](X1,X2) = 2.X2 + 2 [U56](X) = 2 [U91](X1,X2) = 2.X1 + X2 + 1 [U92](X) = 2 [__](X1,X2) = 2.X1 + X2 + 2 [a] = 2 [activate](X) = X [e] = 2 [i] = 1 [isList](X) = 2 [isNeList](X) = 2.X + 2 [isPalListKind](X) = 2.X [isQid](X) = 2.X [nil] = 2 [o] = 2 [u] = 1 [n____](X1,X2) = 2.X1 + X2 + 2 [n__a] = 2 [n__e] = 2 [n__i] = 1 [n__nil] = 2 [n__o] = 2 [n__u] = 1 [tt] = 2 [U11#](X1,X2) = 2.X2 + 2 [U12#](X1,X2) = 2.X2 + 1 [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 + 2 [U25#](X1,X2) = 2.X2 + 2 [U41#](X1,X2,X3) = 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.X2 + 2.X3 + 2 [U45#](X1,X2) = 2.X2 + 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.X2 + 2.X3 + 2 [U54#](X1,X2,X3) = 2.X2 + 2.X3 + 2 [U55#](X1,X2) = X1 + 2.X2 [ISLIST](X) = 2.X + 2 [ISNELIST](X) = 2.X + 1 Problem 1.4: SCC Processor: -> Pairs: U12#(tt,V) -> ISNELIST(activate(V)) U21#(tt,V1,V2) -> U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22#(tt,V1,V2) -> U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23#(tt,V1,V2) -> U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24#(tt,V1,V2) -> U25#(isList(activate(V1)),activate(V2)) U24#(tt,V1,V2) -> ISLIST(activate(V1)) U25#(tt,V2) -> ISLIST(activate(V2)) U41#(tt,V1,V2) -> U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42#(tt,V1,V2) -> U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43#(tt,V1,V2) -> U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44#(tt,V1,V2) -> U45#(isList(activate(V1)),activate(V2)) U44#(tt,V1,V2) -> ISLIST(activate(V1)) U45#(tt,V2) -> ISNELIST(activate(V2)) U51#(tt,V1,V2) -> U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52#(tt,V1,V2) -> U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53#(tt,V1,V2) -> U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54#(tt,V1,V2) -> U55#(isNeList(activate(V1)),activate(V2)) U54#(tt,V1,V2) -> ISNELIST(activate(V1)) U55#(tt,V2) -> ISLIST(activate(V2)) ISLIST(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ISLIST(V) -> U11#(isPalListKind(activate(V)),activate(V)) ISNELIST(n____(V1,V2)) -> U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ISNELIST(n____(V1,V2)) -> U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)) -> Rules: U11(tt,V) -> U12(isPalListKind(activate(V)),activate(V)) U12(tt,V) -> U13(isNeList(activate(V))) U13(tt) -> tt U21(tt,V1,V2) -> U22(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22(tt,V1,V2) -> U23(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23(tt,V1,V2) -> U24(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24(tt,V1,V2) -> U25(isList(activate(V1)),activate(V2)) U25(tt,V2) -> U26(isList(activate(V2))) U26(tt) -> tt U31(tt,V) -> U32(isPalListKind(activate(V)),activate(V)) U32(tt,V) -> U33(isQid(activate(V))) U33(tt) -> tt U41(tt,V1,V2) -> U42(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42(tt,V1,V2) -> U43(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43(tt,V1,V2) -> U44(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44(tt,V1,V2) -> U45(isList(activate(V1)),activate(V2)) U45(tt,V2) -> U46(isNeList(activate(V2))) U46(tt) -> tt U51(tt,V1,V2) -> U52(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52(tt,V1,V2) -> U53(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53(tt,V1,V2) -> U54(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54(tt,V1,V2) -> U55(isNeList(activate(V1)),activate(V2)) U55(tt,V2) -> U56(isList(activate(V2))) U56(tt) -> tt U61(tt,V) -> U62(isPalListKind(activate(V)),activate(V)) U62(tt,V) -> U63(isQid(activate(V))) U63(tt) -> tt U71(tt,I,P) -> U72(isPalListKind(activate(I)),activate(P)) U72(tt,P) -> U73(isPal(activate(P)),activate(P)) U73(tt,P) -> U74(isPalListKind(activate(P))) U74(tt) -> tt U81(tt,V) -> U82(isPalListKind(activate(V)),activate(V)) U82(tt,V) -> U83(isNePal(activate(V))) U83(tt) -> tt U91(tt,V2) -> U92(isPalListKind(activate(V2))) U92(tt) -> tt __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil,X) -> X __(X,nil) -> X __(X1,X2) -> n____(X1,X2) a -> n__a activate(n____(X1,X2)) -> __(X1,X2) activate(n__a) -> a activate(n__e) -> e activate(n__i) -> i activate(n__nil) -> nil activate(n__o) -> o activate(n__u) -> u activate(X) -> X e -> n__e i -> n__i isList(n____(V1,V2)) -> U21(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList(n__nil) -> tt isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,__(P,I))) -> U71(isQid(activate(I)),activate(I),activate(P)) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isPal(n__nil) -> tt isPal(V) -> U81(isPalListKind(activate(V)),activate(V)) isPalListKind(n____(V1,V2)) -> U91(isPalListKind(activate(V1)),activate(V2)) isPalListKind(n__a) -> tt isPalListKind(n__e) -> tt isPalListKind(n__i) -> tt isPalListKind(n__nil) -> tt isPalListKind(n__o) -> tt isPalListKind(n__u) -> tt isQid(n__a) -> tt isQid(n__e) -> tt isQid(n__i) -> tt isQid(n__o) -> tt isQid(n__u) -> tt nil -> n__nil o -> n__o u -> n__u ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: U21#(tt,V1,V2) -> U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22#(tt,V1,V2) -> U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23#(tt,V1,V2) -> U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24#(tt,V1,V2) -> U25#(isList(activate(V1)),activate(V2)) U24#(tt,V1,V2) -> ISLIST(activate(V1)) U25#(tt,V2) -> ISLIST(activate(V2)) ISLIST(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ->->-> Rules: U11(tt,V) -> U12(isPalListKind(activate(V)),activate(V)) U12(tt,V) -> U13(isNeList(activate(V))) U13(tt) -> tt U21(tt,V1,V2) -> U22(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22(tt,V1,V2) -> U23(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23(tt,V1,V2) -> U24(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24(tt,V1,V2) -> U25(isList(activate(V1)),activate(V2)) U25(tt,V2) -> U26(isList(activate(V2))) U26(tt) -> tt U31(tt,V) -> U32(isPalListKind(activate(V)),activate(V)) U32(tt,V) -> U33(isQid(activate(V))) U33(tt) -> tt U41(tt,V1,V2) -> U42(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42(tt,V1,V2) -> U43(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43(tt,V1,V2) -> U44(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44(tt,V1,V2) -> U45(isList(activate(V1)),activate(V2)) U45(tt,V2) -> U46(isNeList(activate(V2))) U46(tt) -> tt U51(tt,V1,V2) -> U52(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52(tt,V1,V2) -> U53(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53(tt,V1,V2) -> U54(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54(tt,V1,V2) -> U55(isNeList(activate(V1)),activate(V2)) U55(tt,V2) -> U56(isList(activate(V2))) U56(tt) -> tt U61(tt,V) -> U62(isPalListKind(activate(V)),activate(V)) U62(tt,V) -> U63(isQid(activate(V))) U63(tt) -> tt U71(tt,I,P) -> U72(isPalListKind(activate(I)),activate(P)) U72(tt,P) -> U73(isPal(activate(P)),activate(P)) U73(tt,P) -> U74(isPalListKind(activate(P))) U74(tt) -> tt U81(tt,V) -> U82(isPalListKind(activate(V)),activate(V)) U82(tt,V) -> U83(isNePal(activate(V))) U83(tt) -> tt U91(tt,V2) -> U92(isPalListKind(activate(V2))) U92(tt) -> tt __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil,X) -> X __(X,nil) -> X __(X1,X2) -> n____(X1,X2) a -> n__a activate(n____(X1,X2)) -> __(X1,X2) activate(n__a) -> a activate(n__e) -> e activate(n__i) -> i activate(n__nil) -> nil activate(n__o) -> o activate(n__u) -> u activate(X) -> X e -> n__e i -> n__i isList(n____(V1,V2)) -> U21(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList(n__nil) -> tt isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,__(P,I))) -> U71(isQid(activate(I)),activate(I),activate(P)) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isPal(n__nil) -> tt isPal(V) -> U81(isPalListKind(activate(V)),activate(V)) isPalListKind(n____(V1,V2)) -> U91(isPalListKind(activate(V1)),activate(V2)) isPalListKind(n__a) -> tt isPalListKind(n__e) -> tt isPalListKind(n__i) -> tt isPalListKind(n__nil) -> tt isPalListKind(n__o) -> tt isPalListKind(n__u) -> tt isQid(n__a) -> tt isQid(n__e) -> tt isQid(n__i) -> tt isQid(n__o) -> tt isQid(n__u) -> tt nil -> n__nil o -> n__o u -> n__u ->->Cycle: ->->-> Pairs: U41#(tt,V1,V2) -> U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42#(tt,V1,V2) -> U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43#(tt,V1,V2) -> U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44#(tt,V1,V2) -> U45#(isList(activate(V1)),activate(V2)) U45#(tt,V2) -> ISNELIST(activate(V2)) U51#(tt,V1,V2) -> U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52#(tt,V1,V2) -> U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53#(tt,V1,V2) -> U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54#(tt,V1,V2) -> ISNELIST(activate(V1)) ISNELIST(n____(V1,V2)) -> U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ISNELIST(n____(V1,V2)) -> U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ->->-> Rules: U11(tt,V) -> U12(isPalListKind(activate(V)),activate(V)) U12(tt,V) -> U13(isNeList(activate(V))) U13(tt) -> tt U21(tt,V1,V2) -> U22(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22(tt,V1,V2) -> U23(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23(tt,V1,V2) -> U24(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24(tt,V1,V2) -> U25(isList(activate(V1)),activate(V2)) U25(tt,V2) -> U26(isList(activate(V2))) U26(tt) -> tt U31(tt,V) -> U32(isPalListKind(activate(V)),activate(V)) U32(tt,V) -> U33(isQid(activate(V))) U33(tt) -> tt U41(tt,V1,V2) -> U42(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42(tt,V1,V2) -> U43(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43(tt,V1,V2) -> U44(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44(tt,V1,V2) -> U45(isList(activate(V1)),activate(V2)) U45(tt,V2) -> U46(isNeList(activate(V2))) U46(tt) -> tt U51(tt,V1,V2) -> U52(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52(tt,V1,V2) -> U53(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53(tt,V1,V2) -> U54(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54(tt,V1,V2) -> U55(isNeList(activate(V1)),activate(V2)) U55(tt,V2) -> U56(isList(activate(V2))) U56(tt) -> tt U61(tt,V) -> U62(isPalListKind(activate(V)),activate(V)) U62(tt,V) -> U63(isQid(activate(V))) U63(tt) -> tt U71(tt,I,P) -> U72(isPalListKind(activate(I)),activate(P)) U72(tt,P) -> U73(isPal(activate(P)),activate(P)) U73(tt,P) -> U74(isPalListKind(activate(P))) U74(tt) -> tt U81(tt,V) -> U82(isPalListKind(activate(V)),activate(V)) U82(tt,V) -> U83(isNePal(activate(V))) U83(tt) -> tt U91(tt,V2) -> U92(isPalListKind(activate(V2))) U92(tt) -> tt __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil,X) -> X __(X,nil) -> X __(X1,X2) -> n____(X1,X2) a -> n__a activate(n____(X1,X2)) -> __(X1,X2) activate(n__a) -> a activate(n__e) -> e activate(n__i) -> i activate(n__nil) -> nil activate(n__o) -> o activate(n__u) -> u activate(X) -> X e -> n__e i -> n__i isList(n____(V1,V2)) -> U21(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList(n__nil) -> tt isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,__(P,I))) -> U71(isQid(activate(I)),activate(I),activate(P)) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isPal(n__nil) -> tt isPal(V) -> U81(isPalListKind(activate(V)),activate(V)) isPalListKind(n____(V1,V2)) -> U91(isPalListKind(activate(V1)),activate(V2)) isPalListKind(n__a) -> tt isPalListKind(n__e) -> tt isPalListKind(n__i) -> tt isPalListKind(n__nil) -> tt isPalListKind(n__o) -> tt isPalListKind(n__u) -> tt isQid(n__a) -> tt isQid(n__e) -> tt isQid(n__i) -> tt isQid(n__o) -> tt isQid(n__u) -> tt nil -> n__nil o -> n__o u -> n__u The problem is decomposed in 2 subproblems. Problem 1.4.1: Reduction Pair Processor: -> Pairs: U21#(tt,V1,V2) -> U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22#(tt,V1,V2) -> U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23#(tt,V1,V2) -> U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24#(tt,V1,V2) -> U25#(isList(activate(V1)),activate(V2)) U24#(tt,V1,V2) -> ISLIST(activate(V1)) U25#(tt,V2) -> ISLIST(activate(V2)) ISLIST(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)) -> Rules: U11(tt,V) -> U12(isPalListKind(activate(V)),activate(V)) U12(tt,V) -> U13(isNeList(activate(V))) U13(tt) -> tt U21(tt,V1,V2) -> U22(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22(tt,V1,V2) -> U23(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23(tt,V1,V2) -> U24(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24(tt,V1,V2) -> U25(isList(activate(V1)),activate(V2)) U25(tt,V2) -> U26(isList(activate(V2))) U26(tt) -> tt U31(tt,V) -> U32(isPalListKind(activate(V)),activate(V)) U32(tt,V) -> U33(isQid(activate(V))) U33(tt) -> tt U41(tt,V1,V2) -> U42(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42(tt,V1,V2) -> U43(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43(tt,V1,V2) -> U44(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44(tt,V1,V2) -> U45(isList(activate(V1)),activate(V2)) U45(tt,V2) -> U46(isNeList(activate(V2))) U46(tt) -> tt U51(tt,V1,V2) -> U52(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52(tt,V1,V2) -> U53(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53(tt,V1,V2) -> U54(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54(tt,V1,V2) -> U55(isNeList(activate(V1)),activate(V2)) U55(tt,V2) -> U56(isList(activate(V2))) U56(tt) -> tt U61(tt,V) -> U62(isPalListKind(activate(V)),activate(V)) U62(tt,V) -> U63(isQid(activate(V))) U63(tt) -> tt U71(tt,I,P) -> U72(isPalListKind(activate(I)),activate(P)) U72(tt,P) -> U73(isPal(activate(P)),activate(P)) U73(tt,P) -> U74(isPalListKind(activate(P))) U74(tt) -> tt U81(tt,V) -> U82(isPalListKind(activate(V)),activate(V)) U82(tt,V) -> U83(isNePal(activate(V))) U83(tt) -> tt U91(tt,V2) -> U92(isPalListKind(activate(V2))) U92(tt) -> tt __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil,X) -> X __(X,nil) -> X __(X1,X2) -> n____(X1,X2) a -> n__a activate(n____(X1,X2)) -> __(X1,X2) activate(n__a) -> a activate(n__e) -> e activate(n__i) -> i activate(n__nil) -> nil activate(n__o) -> o activate(n__u) -> u activate(X) -> X e -> n__e i -> n__i isList(n____(V1,V2)) -> U21(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList(n__nil) -> tt isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,__(P,I))) -> U71(isQid(activate(I)),activate(I),activate(P)) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isPal(n__nil) -> tt isPal(V) -> U81(isPalListKind(activate(V)),activate(V)) isPalListKind(n____(V1,V2)) -> U91(isPalListKind(activate(V1)),activate(V2)) isPalListKind(n__a) -> tt isPalListKind(n__e) -> tt isPalListKind(n__i) -> tt isPalListKind(n__nil) -> tt isPalListKind(n__o) -> tt isPalListKind(n__u) -> tt isQid(n__a) -> tt isQid(n__e) -> tt isQid(n__i) -> tt isQid(n__o) -> tt isQid(n__u) -> tt nil -> n__nil o -> n__o u -> n__u -> Usable rules: U11(tt,V) -> U12(isPalListKind(activate(V)),activate(V)) U12(tt,V) -> U13(isNeList(activate(V))) U13(tt) -> tt U21(tt,V1,V2) -> U22(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22(tt,V1,V2) -> U23(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23(tt,V1,V2) -> U24(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24(tt,V1,V2) -> U25(isList(activate(V1)),activate(V2)) U25(tt,V2) -> U26(isList(activate(V2))) U26(tt) -> tt U31(tt,V) -> U32(isPalListKind(activate(V)),activate(V)) U32(tt,V) -> U33(isQid(activate(V))) U33(tt) -> tt U41(tt,V1,V2) -> U42(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42(tt,V1,V2) -> U43(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43(tt,V1,V2) -> U44(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44(tt,V1,V2) -> U45(isList(activate(V1)),activate(V2)) U45(tt,V2) -> U46(isNeList(activate(V2))) U46(tt) -> tt U51(tt,V1,V2) -> U52(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52(tt,V1,V2) -> U53(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53(tt,V1,V2) -> U54(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54(tt,V1,V2) -> U55(isNeList(activate(V1)),activate(V2)) U55(tt,V2) -> U56(isList(activate(V2))) U56(tt) -> tt U91(tt,V2) -> U92(isPalListKind(activate(V2))) U92(tt) -> tt __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil,X) -> X __(X,nil) -> X __(X1,X2) -> n____(X1,X2) a -> n__a activate(n____(X1,X2)) -> __(X1,X2) activate(n__a) -> a activate(n__e) -> e activate(n__i) -> i activate(n__nil) -> nil activate(n__o) -> o activate(n__u) -> u activate(X) -> X e -> n__e i -> n__i isList(n____(V1,V2)) -> U21(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList(n__nil) -> tt isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isPalListKind(n____(V1,V2)) -> U91(isPalListKind(activate(V1)),activate(V2)) isPalListKind(n__a) -> tt isPalListKind(n__e) -> tt isPalListKind(n__i) -> tt isPalListKind(n__nil) -> tt isPalListKind(n__o) -> tt isPalListKind(n__u) -> tt isQid(n__a) -> tt isQid(n__e) -> tt isQid(n__i) -> tt isQid(n__o) -> tt isQid(n__u) -> tt nil -> n__nil o -> n__o u -> n__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 [U26](X) = 2 [U31](X1,X2) = 2.X2 + 2 [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 + X2 + 2.X3 + 2 [U43](X1,X2,X3) = X2 + 2.X3 + 2 [U44](X1,X2,X3) = X2 + 2.X3 + 2 [U45](X1,X2) = 2.X2 + 2 [U46](X) = 2 [U51](X1,X2,X3) = 2.X1 + 2.X3 [U52](X1,X2,X3) = 2.X1 + 2.X3 [U53](X1,X2,X3) = X1 + 2.X3 + 2 [U54](X1,X2,X3) = X1 + 2.X3 + 2 [U55](X1,X2) = 2 [U56](X) = 2 [U91](X1,X2) = 2 [U92](X) = 2 [__](X1,X2) = 2.X1 + X2 + 2 [a] = 2 [activate](X) = X [e] = 1 [i] = 2 [isList](X) = 2.X + 2 [isNeList](X) = 2.X + 2 [isPalListKind](X) = 2 [isQid](X) = 2.X [nil] = 2 [o] = 2 [u] = 1 [n____](X1,X2) = 2.X1 + X2 + 2 [n__a] = 2 [n__e] = 1 [n__i] = 2 [n__nil] = 2 [n__o] = 2 [n__u] = 1 [tt] = 2 [U21#](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 1 [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 [ISLIST](X) = 2.X + 2 Problem 1.4.1: SCC Processor: -> Pairs: U22#(tt,V1,V2) -> U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23#(tt,V1,V2) -> U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24#(tt,V1,V2) -> U25#(isList(activate(V1)),activate(V2)) U24#(tt,V1,V2) -> ISLIST(activate(V1)) U25#(tt,V2) -> ISLIST(activate(V2)) ISLIST(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)) -> Rules: U11(tt,V) -> U12(isPalListKind(activate(V)),activate(V)) U12(tt,V) -> U13(isNeList(activate(V))) U13(tt) -> tt U21(tt,V1,V2) -> U22(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22(tt,V1,V2) -> U23(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23(tt,V1,V2) -> U24(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24(tt,V1,V2) -> U25(isList(activate(V1)),activate(V2)) U25(tt,V2) -> U26(isList(activate(V2))) U26(tt) -> tt U31(tt,V) -> U32(isPalListKind(activate(V)),activate(V)) U32(tt,V) -> U33(isQid(activate(V))) U33(tt) -> tt U41(tt,V1,V2) -> U42(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42(tt,V1,V2) -> U43(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43(tt,V1,V2) -> U44(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44(tt,V1,V2) -> U45(isList(activate(V1)),activate(V2)) U45(tt,V2) -> U46(isNeList(activate(V2))) U46(tt) -> tt U51(tt,V1,V2) -> U52(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52(tt,V1,V2) -> U53(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53(tt,V1,V2) -> U54(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54(tt,V1,V2) -> U55(isNeList(activate(V1)),activate(V2)) U55(tt,V2) -> U56(isList(activate(V2))) U56(tt) -> tt U61(tt,V) -> U62(isPalListKind(activate(V)),activate(V)) U62(tt,V) -> U63(isQid(activate(V))) U63(tt) -> tt U71(tt,I,P) -> U72(isPalListKind(activate(I)),activate(P)) U72(tt,P) -> U73(isPal(activate(P)),activate(P)) U73(tt,P) -> U74(isPalListKind(activate(P))) U74(tt) -> tt U81(tt,V) -> U82(isPalListKind(activate(V)),activate(V)) U82(tt,V) -> U83(isNePal(activate(V))) U83(tt) -> tt U91(tt,V2) -> U92(isPalListKind(activate(V2))) U92(tt) -> tt __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil,X) -> X __(X,nil) -> X __(X1,X2) -> n____(X1,X2) a -> n__a activate(n____(X1,X2)) -> __(X1,X2) activate(n__a) -> a activate(n__e) -> e activate(n__i) -> i activate(n__nil) -> nil activate(n__o) -> o activate(n__u) -> u activate(X) -> X e -> n__e i -> n__i isList(n____(V1,V2)) -> U21(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList(n__nil) -> tt isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,__(P,I))) -> U71(isQid(activate(I)),activate(I),activate(P)) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isPal(n__nil) -> tt isPal(V) -> U81(isPalListKind(activate(V)),activate(V)) isPalListKind(n____(V1,V2)) -> U91(isPalListKind(activate(V1)),activate(V2)) isPalListKind(n__a) -> tt isPalListKind(n__e) -> tt isPalListKind(n__i) -> tt isPalListKind(n__nil) -> tt isPalListKind(n__o) -> tt isPalListKind(n__u) -> tt isQid(n__a) -> tt isQid(n__e) -> tt isQid(n__i) -> tt isQid(n__o) -> tt isQid(n__u) -> tt nil -> n__nil o -> n__o u -> n__u ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.4.2: Reduction Pair Processor: -> Pairs: U41#(tt,V1,V2) -> U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42#(tt,V1,V2) -> U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43#(tt,V1,V2) -> U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44#(tt,V1,V2) -> U45#(isList(activate(V1)),activate(V2)) U45#(tt,V2) -> ISNELIST(activate(V2)) U51#(tt,V1,V2) -> U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52#(tt,V1,V2) -> U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53#(tt,V1,V2) -> U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54#(tt,V1,V2) -> ISNELIST(activate(V1)) ISNELIST(n____(V1,V2)) -> U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ISNELIST(n____(V1,V2)) -> U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)) -> Rules: U11(tt,V) -> U12(isPalListKind(activate(V)),activate(V)) U12(tt,V) -> U13(isNeList(activate(V))) U13(tt) -> tt U21(tt,V1,V2) -> U22(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22(tt,V1,V2) -> U23(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23(tt,V1,V2) -> U24(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24(tt,V1,V2) -> U25(isList(activate(V1)),activate(V2)) U25(tt,V2) -> U26(isList(activate(V2))) U26(tt) -> tt U31(tt,V) -> U32(isPalListKind(activate(V)),activate(V)) U32(tt,V) -> U33(isQid(activate(V))) U33(tt) -> tt U41(tt,V1,V2) -> U42(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42(tt,V1,V2) -> U43(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43(tt,V1,V2) -> U44(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44(tt,V1,V2) -> U45(isList(activate(V1)),activate(V2)) U45(tt,V2) -> U46(isNeList(activate(V2))) U46(tt) -> tt U51(tt,V1,V2) -> U52(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52(tt,V1,V2) -> U53(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53(tt,V1,V2) -> U54(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54(tt,V1,V2) -> U55(isNeList(activate(V1)),activate(V2)) U55(tt,V2) -> U56(isList(activate(V2))) U56(tt) -> tt U61(tt,V) -> U62(isPalListKind(activate(V)),activate(V)) U62(tt,V) -> U63(isQid(activate(V))) U63(tt) -> tt U71(tt,I,P) -> U72(isPalListKind(activate(I)),activate(P)) U72(tt,P) -> U73(isPal(activate(P)),activate(P)) U73(tt,P) -> U74(isPalListKind(activate(P))) U74(tt) -> tt U81(tt,V) -> U82(isPalListKind(activate(V)),activate(V)) U82(tt,V) -> U83(isNePal(activate(V))) U83(tt) -> tt U91(tt,V2) -> U92(isPalListKind(activate(V2))) U92(tt) -> tt __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil,X) -> X __(X,nil) -> X __(X1,X2) -> n____(X1,X2) a -> n__a activate(n____(X1,X2)) -> __(X1,X2) activate(n__a) -> a activate(n__e) -> e activate(n__i) -> i activate(n__nil) -> nil activate(n__o) -> o activate(n__u) -> u activate(X) -> X e -> n__e i -> n__i isList(n____(V1,V2)) -> U21(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList(n__nil) -> tt isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,__(P,I))) -> U71(isQid(activate(I)),activate(I),activate(P)) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isPal(n__nil) -> tt isPal(V) -> U81(isPalListKind(activate(V)),activate(V)) isPalListKind(n____(V1,V2)) -> U91(isPalListKind(activate(V1)),activate(V2)) isPalListKind(n__a) -> tt isPalListKind(n__e) -> tt isPalListKind(n__i) -> tt isPalListKind(n__nil) -> tt isPalListKind(n__o) -> tt isPalListKind(n__u) -> tt isQid(n__a) -> tt isQid(n__e) -> tt isQid(n__i) -> tt isQid(n__o) -> tt isQid(n__u) -> tt nil -> n__nil o -> n__o u -> n__u -> Usable rules: U11(tt,V) -> U12(isPalListKind(activate(V)),activate(V)) U12(tt,V) -> U13(isNeList(activate(V))) U13(tt) -> tt U21(tt,V1,V2) -> U22(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22(tt,V1,V2) -> U23(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23(tt,V1,V2) -> U24(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24(tt,V1,V2) -> U25(isList(activate(V1)),activate(V2)) U25(tt,V2) -> U26(isList(activate(V2))) U26(tt) -> tt U31(tt,V) -> U32(isPalListKind(activate(V)),activate(V)) U32(tt,V) -> U33(isQid(activate(V))) U33(tt) -> tt U41(tt,V1,V2) -> U42(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42(tt,V1,V2) -> U43(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43(tt,V1,V2) -> U44(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44(tt,V1,V2) -> U45(isList(activate(V1)),activate(V2)) U45(tt,V2) -> U46(isNeList(activate(V2))) U46(tt) -> tt U51(tt,V1,V2) -> U52(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52(tt,V1,V2) -> U53(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53(tt,V1,V2) -> U54(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54(tt,V1,V2) -> U55(isNeList(activate(V1)),activate(V2)) U55(tt,V2) -> U56(isList(activate(V2))) U56(tt) -> tt U91(tt,V2) -> U92(isPalListKind(activate(V2))) U92(tt) -> tt __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil,X) -> X __(X,nil) -> X __(X1,X2) -> n____(X1,X2) a -> n__a activate(n____(X1,X2)) -> __(X1,X2) activate(n__a) -> a activate(n__e) -> e activate(n__i) -> i activate(n__nil) -> nil activate(n__o) -> o activate(n__u) -> u activate(X) -> X e -> n__e i -> n__i isList(n____(V1,V2)) -> U21(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList(n__nil) -> tt isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isPalListKind(n____(V1,V2)) -> U91(isPalListKind(activate(V1)),activate(V2)) isPalListKind(n__a) -> tt isPalListKind(n__e) -> tt isPalListKind(n__i) -> tt isPalListKind(n__nil) -> tt isPalListKind(n__o) -> tt isPalListKind(n__u) -> tt isQid(n__a) -> tt isQid(n__e) -> tt isQid(n__i) -> tt isQid(n__o) -> tt isQid(n__u) -> tt nil -> n__nil o -> n__o u -> n__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.X3 + 2 [U23](X1,X2,X3) = 2.X1 + 2 [U24](X1,X2,X3) = 2 [U25](X1,X2) = 2 [U26](X) = 2 [U31](X1,X2) = X1 + X2 + 2 [U32](X1,X2) = X1 + 2 [U33](X) = X + 1 [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U42](X1,X2,X3) = X1 + X2 + 2.X3 + 1 [U43](X1,X2,X3) = X2 + 2.X3 + 2 [U44](X1,X2,X3) = 2.X1 + 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.X3 + 2 [U53](X1,X2,X3) = X1 + X3 + 1 [U54](X1,X2,X3) = X1 + 2 [U55](X1,X2) = 2 [U56](X) = 2 [U91](X1,X2) = 2.X1 + X2 + 2 [U92](X) = X + 1 [__](X1,X2) = 2.X1 + X2 + 2 [a] = 2 [activate](X) = X [e] = 2 [i] = 2 [isList](X) = 2.X + 2 [isNeList](X) = 2.X + 2 [isPalListKind](X) = X [isQid](X) = 2 [nil] = 2 [o] = 2 [u] = 2 [n____](X1,X2) = 2.X1 + X2 + 2 [n__a] = 2 [n__e] = 2 [n__i] = 2 [n__nil] = 2 [n__o] = 2 [n__u] = 2 [tt] = 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.X2 + 2.X3 + 2 [U45#](X1,X2) = X1 + 2.X2 [U51#](X1,X2,X3) = X1 + 2.X2 + 2.X3 [U52#](X1,X2,X3) = 2.X2 + 2.X3 + 2 [U53#](X1,X2,X3) = 2.X1 + 2.X2 + 1 [U54#](X1,X2,X3) = 2.X2 + 2 [ISNELIST](X) = 2.X + 2 Problem 1.4.2: SCC Processor: -> Pairs: U42#(tt,V1,V2) -> U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43#(tt,V1,V2) -> U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44#(tt,V1,V2) -> U45#(isList(activate(V1)),activate(V2)) U45#(tt,V2) -> ISNELIST(activate(V2)) U51#(tt,V1,V2) -> U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52#(tt,V1,V2) -> U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53#(tt,V1,V2) -> U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54#(tt,V1,V2) -> ISNELIST(activate(V1)) ISNELIST(n____(V1,V2)) -> U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ISNELIST(n____(V1,V2)) -> U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)) -> Rules: U11(tt,V) -> U12(isPalListKind(activate(V)),activate(V)) U12(tt,V) -> U13(isNeList(activate(V))) U13(tt) -> tt U21(tt,V1,V2) -> U22(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22(tt,V1,V2) -> U23(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23(tt,V1,V2) -> U24(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24(tt,V1,V2) -> U25(isList(activate(V1)),activate(V2)) U25(tt,V2) -> U26(isList(activate(V2))) U26(tt) -> tt U31(tt,V) -> U32(isPalListKind(activate(V)),activate(V)) U32(tt,V) -> U33(isQid(activate(V))) U33(tt) -> tt U41(tt,V1,V2) -> U42(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42(tt,V1,V2) -> U43(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43(tt,V1,V2) -> U44(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44(tt,V1,V2) -> U45(isList(activate(V1)),activate(V2)) U45(tt,V2) -> U46(isNeList(activate(V2))) U46(tt) -> tt U51(tt,V1,V2) -> U52(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52(tt,V1,V2) -> U53(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53(tt,V1,V2) -> U54(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54(tt,V1,V2) -> U55(isNeList(activate(V1)),activate(V2)) U55(tt,V2) -> U56(isList(activate(V2))) U56(tt) -> tt U61(tt,V) -> U62(isPalListKind(activate(V)),activate(V)) U62(tt,V) -> U63(isQid(activate(V))) U63(tt) -> tt U71(tt,I,P) -> U72(isPalListKind(activate(I)),activate(P)) U72(tt,P) -> U73(isPal(activate(P)),activate(P)) U73(tt,P) -> U74(isPalListKind(activate(P))) U74(tt) -> tt U81(tt,V) -> U82(isPalListKind(activate(V)),activate(V)) U82(tt,V) -> U83(isNePal(activate(V))) U83(tt) -> tt U91(tt,V2) -> U92(isPalListKind(activate(V2))) U92(tt) -> tt __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil,X) -> X __(X,nil) -> X __(X1,X2) -> n____(X1,X2) a -> n__a activate(n____(X1,X2)) -> __(X1,X2) activate(n__a) -> a activate(n__e) -> e activate(n__i) -> i activate(n__nil) -> nil activate(n__o) -> o activate(n__u) -> u activate(X) -> X e -> n__e i -> n__i isList(n____(V1,V2)) -> U21(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList(n__nil) -> tt isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,__(P,I))) -> U71(isQid(activate(I)),activate(I),activate(P)) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isPal(n__nil) -> tt isPal(V) -> U81(isPalListKind(activate(V)),activate(V)) isPalListKind(n____(V1,V2)) -> U91(isPalListKind(activate(V1)),activate(V2)) isPalListKind(n__a) -> tt isPalListKind(n__e) -> tt isPalListKind(n__i) -> tt isPalListKind(n__nil) -> tt isPalListKind(n__o) -> tt isPalListKind(n__u) -> tt isQid(n__a) -> tt isQid(n__e) -> tt isQid(n__i) -> tt isQid(n__o) -> tt isQid(n__u) -> tt nil -> n__nil o -> n__o u -> n__u ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: U51#(tt,V1,V2) -> U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52#(tt,V1,V2) -> U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53#(tt,V1,V2) -> U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54#(tt,V1,V2) -> ISNELIST(activate(V1)) ISNELIST(n____(V1,V2)) -> U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ->->-> Rules: U11(tt,V) -> U12(isPalListKind(activate(V)),activate(V)) U12(tt,V) -> U13(isNeList(activate(V))) U13(tt) -> tt U21(tt,V1,V2) -> U22(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22(tt,V1,V2) -> U23(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23(tt,V1,V2) -> U24(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24(tt,V1,V2) -> U25(isList(activate(V1)),activate(V2)) U25(tt,V2) -> U26(isList(activate(V2))) U26(tt) -> tt U31(tt,V) -> U32(isPalListKind(activate(V)),activate(V)) U32(tt,V) -> U33(isQid(activate(V))) U33(tt) -> tt U41(tt,V1,V2) -> U42(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42(tt,V1,V2) -> U43(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43(tt,V1,V2) -> U44(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44(tt,V1,V2) -> U45(isList(activate(V1)),activate(V2)) U45(tt,V2) -> U46(isNeList(activate(V2))) U46(tt) -> tt U51(tt,V1,V2) -> U52(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52(tt,V1,V2) -> U53(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53(tt,V1,V2) -> U54(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54(tt,V1,V2) -> U55(isNeList(activate(V1)),activate(V2)) U55(tt,V2) -> U56(isList(activate(V2))) U56(tt) -> tt U61(tt,V) -> U62(isPalListKind(activate(V)),activate(V)) U62(tt,V) -> U63(isQid(activate(V))) U63(tt) -> tt U71(tt,I,P) -> U72(isPalListKind(activate(I)),activate(P)) U72(tt,P) -> U73(isPal(activate(P)),activate(P)) U73(tt,P) -> U74(isPalListKind(activate(P))) U74(tt) -> tt U81(tt,V) -> U82(isPalListKind(activate(V)),activate(V)) U82(tt,V) -> U83(isNePal(activate(V))) U83(tt) -> tt U91(tt,V2) -> U92(isPalListKind(activate(V2))) U92(tt) -> tt __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil,X) -> X __(X,nil) -> X __(X1,X2) -> n____(X1,X2) a -> n__a activate(n____(X1,X2)) -> __(X1,X2) activate(n__a) -> a activate(n__e) -> e activate(n__i) -> i activate(n__nil) -> nil activate(n__o) -> o activate(n__u) -> u activate(X) -> X e -> n__e i -> n__i isList(n____(V1,V2)) -> U21(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList(n__nil) -> tt isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,__(P,I))) -> U71(isQid(activate(I)),activate(I),activate(P)) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isPal(n__nil) -> tt isPal(V) -> U81(isPalListKind(activate(V)),activate(V)) isPalListKind(n____(V1,V2)) -> U91(isPalListKind(activate(V1)),activate(V2)) isPalListKind(n__a) -> tt isPalListKind(n__e) -> tt isPalListKind(n__i) -> tt isPalListKind(n__nil) -> tt isPalListKind(n__o) -> tt isPalListKind(n__u) -> tt isQid(n__a) -> tt isQid(n__e) -> tt isQid(n__i) -> tt isQid(n__o) -> tt isQid(n__u) -> tt nil -> n__nil o -> n__o u -> n__u Problem 1.4.2: Reduction Pair Processor: -> Pairs: U51#(tt,V1,V2) -> U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52#(tt,V1,V2) -> U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53#(tt,V1,V2) -> U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54#(tt,V1,V2) -> ISNELIST(activate(V1)) ISNELIST(n____(V1,V2)) -> U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)) -> Rules: U11(tt,V) -> U12(isPalListKind(activate(V)),activate(V)) U12(tt,V) -> U13(isNeList(activate(V))) U13(tt) -> tt U21(tt,V1,V2) -> U22(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22(tt,V1,V2) -> U23(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23(tt,V1,V2) -> U24(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24(tt,V1,V2) -> U25(isList(activate(V1)),activate(V2)) U25(tt,V2) -> U26(isList(activate(V2))) U26(tt) -> tt U31(tt,V) -> U32(isPalListKind(activate(V)),activate(V)) U32(tt,V) -> U33(isQid(activate(V))) U33(tt) -> tt U41(tt,V1,V2) -> U42(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42(tt,V1,V2) -> U43(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43(tt,V1,V2) -> U44(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44(tt,V1,V2) -> U45(isList(activate(V1)),activate(V2)) U45(tt,V2) -> U46(isNeList(activate(V2))) U46(tt) -> tt U51(tt,V1,V2) -> U52(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52(tt,V1,V2) -> U53(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53(tt,V1,V2) -> U54(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54(tt,V1,V2) -> U55(isNeList(activate(V1)),activate(V2)) U55(tt,V2) -> U56(isList(activate(V2))) U56(tt) -> tt U61(tt,V) -> U62(isPalListKind(activate(V)),activate(V)) U62(tt,V) -> U63(isQid(activate(V))) U63(tt) -> tt U71(tt,I,P) -> U72(isPalListKind(activate(I)),activate(P)) U72(tt,P) -> U73(isPal(activate(P)),activate(P)) U73(tt,P) -> U74(isPalListKind(activate(P))) U74(tt) -> tt U81(tt,V) -> U82(isPalListKind(activate(V)),activate(V)) U82(tt,V) -> U83(isNePal(activate(V))) U83(tt) -> tt U91(tt,V2) -> U92(isPalListKind(activate(V2))) U92(tt) -> tt __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil,X) -> X __(X,nil) -> X __(X1,X2) -> n____(X1,X2) a -> n__a activate(n____(X1,X2)) -> __(X1,X2) activate(n__a) -> a activate(n__e) -> e activate(n__i) -> i activate(n__nil) -> nil activate(n__o) -> o activate(n__u) -> u activate(X) -> X e -> n__e i -> n__i isList(n____(V1,V2)) -> U21(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList(n__nil) -> tt isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,__(P,I))) -> U71(isQid(activate(I)),activate(I),activate(P)) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isPal(n__nil) -> tt isPal(V) -> U81(isPalListKind(activate(V)),activate(V)) isPalListKind(n____(V1,V2)) -> U91(isPalListKind(activate(V1)),activate(V2)) isPalListKind(n__a) -> tt isPalListKind(n__e) -> tt isPalListKind(n__i) -> tt isPalListKind(n__nil) -> tt isPalListKind(n__o) -> tt isPalListKind(n__u) -> tt isQid(n__a) -> tt isQid(n__e) -> tt isQid(n__i) -> tt isQid(n__o) -> tt isQid(n__u) -> tt nil -> n__nil o -> n__o u -> n__u -> Usable rules: U91(tt,V2) -> U92(isPalListKind(activate(V2))) U92(tt) -> tt __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil,X) -> X __(X,nil) -> X __(X1,X2) -> n____(X1,X2) a -> n__a activate(n____(X1,X2)) -> __(X1,X2) activate(n__a) -> a activate(n__e) -> e activate(n__i) -> i activate(n__nil) -> nil activate(n__o) -> o activate(n__u) -> u activate(X) -> X e -> n__e i -> n__i isPalListKind(n____(V1,V2)) -> U91(isPalListKind(activate(V1)),activate(V2)) isPalListKind(n__a) -> tt isPalListKind(n__e) -> tt isPalListKind(n__i) -> tt isPalListKind(n__nil) -> tt isPalListKind(n__o) -> tt isPalListKind(n__u) -> tt nil -> n__nil o -> n__o u -> n__u ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U91](X1,X2) = 2 [U92](X) = X [__](X1,X2) = 2.X1 + X2 + 2 [a] = 1 [activate](X) = X [e] = 2 [i] = 2 [isPalListKind](X) = 2 [nil] = 2 [o] = 2 [u] = 2 [n____](X1,X2) = 2.X1 + X2 + 2 [n__a] = 1 [n__e] = 2 [n__i] = 2 [n__nil] = 2 [n__o] = 2 [n__u] = 2 [tt] = 2 [U51#](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 1 [U52#](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 [U53#](X1,X2,X3) = 2.X1 + 2.X2 [U54#](X1,X2,X3) = X1 + 2.X2 + 2 [ISNELIST](X) = 2.X + 1 Problem 1.4.2: SCC Processor: -> Pairs: U52#(tt,V1,V2) -> U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53#(tt,V1,V2) -> U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54#(tt,V1,V2) -> ISNELIST(activate(V1)) ISNELIST(n____(V1,V2)) -> U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)) -> Rules: U11(tt,V) -> U12(isPalListKind(activate(V)),activate(V)) U12(tt,V) -> U13(isNeList(activate(V))) U13(tt) -> tt U21(tt,V1,V2) -> U22(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22(tt,V1,V2) -> U23(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23(tt,V1,V2) -> U24(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24(tt,V1,V2) -> U25(isList(activate(V1)),activate(V2)) U25(tt,V2) -> U26(isList(activate(V2))) U26(tt) -> tt U31(tt,V) -> U32(isPalListKind(activate(V)),activate(V)) U32(tt,V) -> U33(isQid(activate(V))) U33(tt) -> tt U41(tt,V1,V2) -> U42(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42(tt,V1,V2) -> U43(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43(tt,V1,V2) -> U44(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44(tt,V1,V2) -> U45(isList(activate(V1)),activate(V2)) U45(tt,V2) -> U46(isNeList(activate(V2))) U46(tt) -> tt U51(tt,V1,V2) -> U52(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52(tt,V1,V2) -> U53(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53(tt,V1,V2) -> U54(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54(tt,V1,V2) -> U55(isNeList(activate(V1)),activate(V2)) U55(tt,V2) -> U56(isList(activate(V2))) U56(tt) -> tt U61(tt,V) -> U62(isPalListKind(activate(V)),activate(V)) U62(tt,V) -> U63(isQid(activate(V))) U63(tt) -> tt U71(tt,I,P) -> U72(isPalListKind(activate(I)),activate(P)) U72(tt,P) -> U73(isPal(activate(P)),activate(P)) U73(tt,P) -> U74(isPalListKind(activate(P))) U74(tt) -> tt U81(tt,V) -> U82(isPalListKind(activate(V)),activate(V)) U82(tt,V) -> U83(isNePal(activate(V))) U83(tt) -> tt U91(tt,V2) -> U92(isPalListKind(activate(V2))) U92(tt) -> tt __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil,X) -> X __(X,nil) -> X __(X1,X2) -> n____(X1,X2) a -> n__a activate(n____(X1,X2)) -> __(X1,X2) activate(n__a) -> a activate(n__e) -> e activate(n__i) -> i activate(n__nil) -> nil activate(n__o) -> o activate(n__u) -> u activate(X) -> X e -> n__e i -> n__i isList(n____(V1,V2)) -> U21(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList(n__nil) -> tt isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,__(P,I))) -> U71(isQid(activate(I)),activate(I),activate(P)) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isPal(n__nil) -> tt isPal(V) -> U81(isPalListKind(activate(V)),activate(V)) isPalListKind(n____(V1,V2)) -> U91(isPalListKind(activate(V1)),activate(V2)) isPalListKind(n__a) -> tt isPalListKind(n__e) -> tt isPalListKind(n__i) -> tt isPalListKind(n__nil) -> tt isPalListKind(n__o) -> tt isPalListKind(n__u) -> tt isQid(n__a) -> tt isQid(n__e) -> tt isQid(n__i) -> tt isQid(n__o) -> tt isQid(n__u) -> tt nil -> n__nil o -> n__o u -> n__u ->Strongly Connected Components: There is no strongly connected component The problem is finite.