/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


--------------------------------------------------------------------------------


YES

Problem 1: 

(VAR I P V V1 V2 X X1 X2 Y Z)
(RULES
U11(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)) -> __(activate(X1),activate(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,n____(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)) -> __#(activate(X1),activate(X2))
 ACTIVATE(n____(X1,X2)) -> ACTIVATE(X1)
 ACTIVATE(n____(X1,X2)) -> ACTIVATE(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,n____(P,I))) -> U71#(isQid(activate(I)),activate(I),activate(P))
 ISNEPAL(n____(I,n____(P,I))) -> ACTIVATE(I)
 ISNEPAL(n____(I,n____(P,I))) -> ACTIVATE(P)
 ISNEPAL(n____(I,n____(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)) -> __(activate(X1),activate(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,n____(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)) -> __#(activate(X1),activate(X2))
 ACTIVATE(n____(X1,X2)) -> ACTIVATE(X1)
 ACTIVATE(n____(X1,X2)) -> ACTIVATE(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,n____(P,I))) -> U71#(isQid(activate(I)),activate(I),activate(P))
 ISNEPAL(n____(I,n____(P,I))) -> ACTIVATE(I)
 ISNEPAL(n____(I,n____(P,I))) -> ACTIVATE(P)
 ISNEPAL(n____(I,n____(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)) -> __(activate(X1),activate(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,n____(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)) -> __(activate(X1),activate(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,n____(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:
 ACTIVATE(n____(X1,X2)) -> ACTIVATE(X1)
 ACTIVATE(n____(X1,X2)) -> ACTIVATE(X2)
->->-> 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)) -> __(activate(X1),activate(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,n____(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)) -> __(activate(X1),activate(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,n____(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,n____(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)) -> __(activate(X1),activate(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,n____(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)) -> __(activate(X1),activate(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,n____(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 5 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)) -> __(activate(X1),activate(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,n____(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)) -> __(activate(X1),activate(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,n____(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: 

Subterm Processor:
-> Pairs:
 ACTIVATE(n____(X1,X2)) -> ACTIVATE(X1)
 ACTIVATE(n____(X1,X2)) -> ACTIVATE(X2)
-> 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)) -> __(activate(X1),activate(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,n____(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(ACTIVATE) = 1

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)) -> __(activate(X1),activate(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,n____(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:
 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)) -> __(activate(X1),activate(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,n____(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)) -> __(activate(X1),activate(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.X1 + 2.X2 + 2
[U92](X) = X
[__](X1,X2) = 2.X1 + X2 + 2
[a] = 2
[activate](X) = X
[e] = 2
[i] = 2
[isPalListKind](X) = 2.X
[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
[U91#](X1,X2) = 2.X1 + 2.X2 + 2
[ISPALLISTKIND](X) = 2.X + 2

Problem 1.3: 

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)) -> __(activate(X1),activate(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,n____(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)) -> __(activate(X1),activate(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,n____(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 1.3: 

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)) -> __(activate(X1),activate(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,n____(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)) -> __(activate(X1),activate(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] = 2
[activate](X) = 2.X + 1
[e] = 2
[i] = 2
[nil] = 2
[o] = 2
[u] = 2
[n____](X1,X2) = 2.X1 + X2 + 2
[n__a] = 2
[n__e] = 2
[n__i] = 1
[n__nil] = 2
[n__o] = 1
[n__u] = 1
[ISPALLISTKIND](X) = 2.X

Problem 1.3: 

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)) -> __(activate(X1),activate(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,n____(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:
 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,n____(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)) -> __(activate(X1),activate(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,n____(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)) -> __(activate(X1),activate(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 + 2.X2 + 2
[U92](X) = X + 2
[__](X1,X2) = 2.X1 + X2 + 2
[a] = 2
[activate](X) = X
[e] = 2
[i] = 2
[isPalListKind](X) = 2.X
[isQid](X) = 2.X + 1
[nil] = 2
[o] = 1
[u] = 2
[n____](X1,X2) = 2.X1 + X2 + 2
[n__a] = 2
[n__e] = 2
[n__i] = 2
[n__nil] = 2
[n__o] = 1
[n__u] = 2
[tt] = 2
[U71#](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2
[U72#](X1,X2) = X1 + 2.X2 + 2
[U81#](X1,X2) = 2.X2 + 2
[U82#](X1,X2) = 2.X2 + 2
[ISNEPAL](X) = 2.X + 2
[ISPAL](X) = 2.X + 2

Problem 1.4: 

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,n____(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)) -> __(activate(X1),activate(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,n____(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 1.5: 

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)) -> __(activate(X1),activate(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,n____(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)) -> __(activate(X1),activate(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) = X2 + 2
[U12](X1,X2) = X1 + X2
[U13](X) = 2
[U21](X1,X2,X3) = X1 + 2.X2 + X3 + 2
[U22](X1,X2,X3) = X1 + 2.X2 + X3 + 2
[U23](X1,X2,X3) = X1 + 2.X2 + X3 + 2
[U24](X1,X2,X3) = 2.X1 + 2.X2 + X3
[U25](X1,X2) = X1 + X2
[U26](X) = X
[U31](X1,X2) = 2.X2 + 2
[U32](X1,X2) = 2.X2 + 2
[U33](X) = 2
[U41](X1,X2,X3) = 2.X1 + 2.X3 + 2
[U42](X1,X2,X3) = 2.X1 + 2.X3 + 2
[U43](X1,X2,X3) = 2.X1 + 2.X3 + 2
[U44](X1,X2,X3) = 2.X1 + 2.X3 + 2
[U45](X1,X2) = 2.X2 + 2
[U46](X) = X
[U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3
[U52](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3
[U53](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3
[U54](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3
[U55](X1,X2) = X1 + 2.X2 + 2
[U56](X) = 2.X
[U91](X1,X2) = X1
[U92](X) = 2
[__](X1,X2) = 2.X1 + X2 + 2
[a] = 2
[activate](X) = X
[e] = 2
[i] = 2
[isList](X) = X + 2
[isNeList](X) = 2.X + 2
[isPalListKind](X) = 2
[isQid](X) = 2.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
[U11#](X1,X2) = X1 + 2.X2
[U12#](X1,X2) = 2.X2 + 1
[U21#](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2
[U22#](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2
[U23#](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2
[U24#](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2
[U25#](X1,X2) = 2.X1 + 2.X2
[U41#](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 1
[U42#](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 1
[U43#](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2
[U44#](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3
[U45#](X1,X2) = 2.X2 + 1
[U51#](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 1
[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
[ISLIST](X) = 2.X + 2
[ISNELIST](X) = 2.X + 1

Problem 1.5: 

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)) -> __(activate(X1),activate(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,n____(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)) -> __(activate(X1),activate(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,n____(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)) -> __(activate(X1),activate(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,n____(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 1.5.1: 

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)) -> __(activate(X1),activate(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,n____(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)) -> __(activate(X1),activate(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.X2 + 2.X3 + 2
[U23](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2
[U24](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2
[U25](X1,X2) = X1
[U26](X) = 2
[U31](X1,X2) = 2.X2 + 2
[U32](X1,X2) = X1 + 2.X2
[U33](X) = 2.X + 1
[U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 1
[U42](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3
[U43](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2
[U44](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 1
[U45](X1,X2) = X1 + 2.X2
[U46](X) = 2
[U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2
[U52](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 1
[U53](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2
[U54](X1,X2,X3) = 2.X2 + X3 + 2
[U55](X1,X2) = X2 + 2
[U56](X) = 2
[U91](X1,X2) = X1
[U92](X) = X
[__](X1,X2) = X1 + X2 + 2
[a] = 2
[activate](X) = X
[e] = 2
[i] = 2
[isList](X) = 2.X + 2
[isNeList](X) = 2.X + 2
[isPalListKind](X) = 2
[isQid](X) = X
[nil] = 2
[o] = 2
[u] = 2
[n____](X1,X2) = X1 + X2 + 2
[n__a] = 2
[n__e] = 2
[n__i] = 2
[n__nil] = 2
[n__o] = 2
[n__u] = 2
[tt] = 2
[U21#](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2
[U22#](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 1
[U23#](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 1
[U24#](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2
[U25#](X1,X2) = X1 + 2.X2 + 2
[ISLIST](X) = 2.X + 2

Problem 1.5.1: 

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)) -> __(activate(X1),activate(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,n____(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 1.5.2: 

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)) -> __(activate(X1),activate(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,n____(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)) -> __(activate(X1),activate(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) = 2
[U21](X1,X2,X3) = 2.X1 + 2.X3 + 2
[U22](X1,X2,X3) = 2.X3 + 2
[U23](X1,X2,X3) = 2.X3 + 2
[U24](X1,X2,X3) = 2.X1 + 2
[U25](X1,X2) = 2
[U26](X) = 2
[U31](X1,X2) = 2.X2 + 2
[U32](X1,X2) = 2.X1 + 2
[U33](X) = X + 2
[U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2
[U42](X1,X2,X3) = 2.X1 + 2.X3 + 1
[U43](X1,X2,X3) = 2.X1 + 2
[U44](X1,X2,X3) = 2
[U45](X1,X2) = 2
[U46](X) = 2
[U51](X1,X2,X3) = X1 + 2.X3
[U52](X1,X2,X3) = 2.X3 + 2
[U53](X1,X2,X3) = 2.X3 + 2
[U54](X1,X2,X3) = 2.X1 + 2
[U55](X1,X2) = 2
[U56](X) = 2
[U91](X1,X2) = 2.X1 + X2 + 2
[U92](X) = 2
[__](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) = X1 + X2 + 2.X3 + 1
[U43#](X1,X2,X3) = X2 + 2.X3 + 2
[U44#](X1,X2,X3) = X2 + 2.X3 + 2
[U45#](X1,X2) = 2.X2 + 2
[U51#](X1,X2,X3) = 2.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.X1 + 2.X2 + 2
[ISNELIST](X) = 2.X + 2

Problem 1.5.2: 

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)) -> __(activate(X1),activate(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,n____(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)) -> __(activate(X1),activate(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,n____(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 1.5.2: 

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)) -> __(activate(X1),activate(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,n____(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)) -> __(activate(X1),activate(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) = X1 + 2.X2 + 1
[U92](X) = X + 1
[__](X1,X2) = 2.X1 + X2 + 1
[a] = 2
[activate](X) = X
[e] = 2
[i] = 2
[isPalListKind](X) = 2.X + 2
[nil] = 2
[o] = 2
[u] = 2
[n____](X1,X2) = 2.X1 + X2 + 1
[n__a] = 2
[n__e] = 2
[n__i] = 2
[n__nil] = 2
[n__o] = 2
[n__u] = 2
[tt] = 2
[U51#](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2
[U52#](X1,X2,X3) = 2.X2 + 2.X3 + 2
[U53#](X1,X2,X3) = X1 + 2.X2
[U54#](X1,X2,X3) = 2.X2 + 2
[ISNELIST](X) = 2.X + 2

Problem 1.5.2: 

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)) -> __(activate(X1),activate(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,n____(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.