YES

Problem 1: 

(VAR v_NonEmpty:S I:S P:S V:S V1:S V2:S X:S X1:S X2:S Y:S Z:S)
(RULES
U11(active(X:S)) -> U11(X:S)
U11(mark(X:S)) -> U11(X:S)
U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
U22(active(X:S)) -> U22(X:S)
U22(mark(X:S)) -> U22(X:S)
U31(active(X:S)) -> U31(X:S)
U31(mark(X:S)) -> U31(X:S)
U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
U42(active(X:S)) -> U42(X:S)
U42(mark(X:S)) -> U42(X:S)
U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
U52(active(X:S)) -> U52(X:S)
U52(mark(X:S)) -> U52(X:S)
U61(active(X:S)) -> U61(X:S)
U61(mark(X:S)) -> U61(X:S)
U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
U72(active(X:S)) -> U72(X:S)
U72(mark(X:S)) -> U72(X:S)
U81(active(X:S)) -> U81(X:S)
U81(mark(X:S)) -> U81(X:S)
__(active(X1:S),X2:S) -> __(X1:S,X2:S)
__(mark(X1:S),X2:S) -> __(X1:S,X2:S)
__(X1:S,active(X2:S)) -> __(X1:S,X2:S)
__(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
active(U11(tt)) -> mark(tt)
active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
active(U22(tt)) -> mark(tt)
active(U31(tt)) -> mark(tt)
active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
active(U42(tt)) -> mark(tt)
active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
active(U52(tt)) -> mark(tt)
active(U61(tt)) -> mark(tt)
active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
active(U72(tt)) -> mark(tt)
active(U81(tt)) -> mark(tt)
active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
active(__(nil,X:S)) -> mark(X:S)
active(__(X:S,nil)) -> mark(X:S)
active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
active(isList(nil)) -> mark(tt)
active(isList(V:S)) -> mark(U11(isNeList(V:S)))
active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
active(isPal(nil)) -> mark(tt)
active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
active(isQid(a)) -> mark(tt)
active(isQid(e)) -> mark(tt)
active(isQid(i)) -> mark(tt)
active(isQid(o)) -> mark(tt)
active(isQid(u)) -> mark(tt)
isList(active(X:S)) -> isList(X:S)
isList(mark(X:S)) -> isList(X:S)
isNeList(active(X:S)) -> isNeList(X:S)
isNeList(mark(X:S)) -> isNeList(X:S)
isNePal(active(X:S)) -> isNePal(X:S)
isNePal(mark(X:S)) -> isNePal(X:S)
isPal(active(X:S)) -> isPal(X:S)
isPal(mark(X:S)) -> isPal(X:S)
isQid(active(X:S)) -> isQid(X:S)
isQid(mark(X:S)) -> isQid(X:S)
mark(U11(X:S)) -> active(U11(mark(X:S)))
mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
mark(U22(X:S)) -> active(U22(mark(X:S)))
mark(U31(X:S)) -> active(U31(mark(X:S)))
mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
mark(U42(X:S)) -> active(U42(mark(X:S)))
mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
mark(U52(X:S)) -> active(U52(mark(X:S)))
mark(U61(X:S)) -> active(U61(mark(X:S)))
mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
mark(U72(X:S)) -> active(U72(mark(X:S)))
mark(U81(X:S)) -> active(U81(mark(X:S)))
mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
mark(isList(X:S)) -> active(isList(X:S))
mark(isNeList(X:S)) -> active(isNeList(X:S))
mark(isNePal(X:S)) -> active(isNePal(X:S))
mark(isPal(X:S)) -> active(isPal(X:S))
mark(isQid(X:S)) -> active(isQid(X:S))
mark(a) -> active(a)
mark(e) -> active(e)
mark(i) -> active(i)
mark(nil) -> active(nil)
mark(o) -> active(o)
mark(tt) -> active(tt)
mark(u) -> active(u)
) 
(STRATEGY INNERMOST)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 U11#(active(X:S)) -> U11#(X:S)
 U11#(mark(X:S)) -> U11#(X:S)
 U21#(active(X1:S),X2:S) -> U21#(X1:S,X2:S)
 U21#(mark(X1:S),X2:S) -> U21#(X1:S,X2:S)
 U21#(X1:S,active(X2:S)) -> U21#(X1:S,X2:S)
 U21#(X1:S,mark(X2:S)) -> U21#(X1:S,X2:S)
 U22#(active(X:S)) -> U22#(X:S)
 U22#(mark(X:S)) -> U22#(X:S)
 U31#(active(X:S)) -> U31#(X:S)
 U31#(mark(X:S)) -> U31#(X:S)
 U41#(active(X1:S),X2:S) -> U41#(X1:S,X2:S)
 U41#(mark(X1:S),X2:S) -> U41#(X1:S,X2:S)
 U41#(X1:S,active(X2:S)) -> U41#(X1:S,X2:S)
 U41#(X1:S,mark(X2:S)) -> U41#(X1:S,X2:S)
 U42#(active(X:S)) -> U42#(X:S)
 U42#(mark(X:S)) -> U42#(X:S)
 U51#(active(X1:S),X2:S) -> U51#(X1:S,X2:S)
 U51#(mark(X1:S),X2:S) -> U51#(X1:S,X2:S)
 U51#(X1:S,active(X2:S)) -> U51#(X1:S,X2:S)
 U51#(X1:S,mark(X2:S)) -> U51#(X1:S,X2:S)
 U52#(active(X:S)) -> U52#(X:S)
 U52#(mark(X:S)) -> U52#(X:S)
 U61#(active(X:S)) -> U61#(X:S)
 U61#(mark(X:S)) -> U61#(X:S)
 U71#(active(X1:S),X2:S) -> U71#(X1:S,X2:S)
 U71#(mark(X1:S),X2:S) -> U71#(X1:S,X2:S)
 U71#(X1:S,active(X2:S)) -> U71#(X1:S,X2:S)
 U71#(X1:S,mark(X2:S)) -> U71#(X1:S,X2:S)
 U72#(active(X:S)) -> U72#(X:S)
 U72#(mark(X:S)) -> U72#(X:S)
 U81#(active(X:S)) -> U81#(X:S)
 U81#(mark(X:S)) -> U81#(X:S)
 __#(active(X1:S),X2:S) -> __#(X1:S,X2:S)
 __#(mark(X1:S),X2:S) -> __#(X1:S,X2:S)
 __#(X1:S,active(X2:S)) -> __#(X1:S,X2:S)
 __#(X1:S,mark(X2:S)) -> __#(X1:S,X2:S)
 ACTIVE(U11(tt)) -> MARK(tt)
 ACTIVE(U21(tt,V2:S)) -> U22#(isList(V2:S))
 ACTIVE(U21(tt,V2:S)) -> ISLIST(V2:S)
 ACTIVE(U21(tt,V2:S)) -> MARK(U22(isList(V2:S)))
 ACTIVE(U22(tt)) -> MARK(tt)
 ACTIVE(U31(tt)) -> MARK(tt)
 ACTIVE(U41(tt,V2:S)) -> U42#(isNeList(V2:S))
 ACTIVE(U41(tt,V2:S)) -> ISNELIST(V2:S)
 ACTIVE(U41(tt,V2:S)) -> MARK(U42(isNeList(V2:S)))
 ACTIVE(U42(tt)) -> MARK(tt)
 ACTIVE(U51(tt,V2:S)) -> U52#(isList(V2:S))
 ACTIVE(U51(tt,V2:S)) -> ISLIST(V2:S)
 ACTIVE(U51(tt,V2:S)) -> MARK(U52(isList(V2:S)))
 ACTIVE(U52(tt)) -> MARK(tt)
 ACTIVE(U61(tt)) -> MARK(tt)
 ACTIVE(U71(tt,P:S)) -> U72#(isPal(P:S))
 ACTIVE(U71(tt,P:S)) -> ISPAL(P:S)
 ACTIVE(U71(tt,P:S)) -> MARK(U72(isPal(P:S)))
 ACTIVE(U72(tt)) -> MARK(tt)
 ACTIVE(U81(tt)) -> MARK(tt)
 ACTIVE(__(__(X:S,Y:S),Z:S)) -> __#(X:S,__(Y:S,Z:S))
 ACTIVE(__(__(X:S,Y:S),Z:S)) -> __#(Y:S,Z:S)
 ACTIVE(__(__(X:S,Y:S),Z:S)) -> MARK(__(X:S,__(Y:S,Z:S)))
 ACTIVE(__(nil,X:S)) -> MARK(X:S)
 ACTIVE(__(X:S,nil)) -> MARK(X:S)
 ACTIVE(isList(__(V1:S,V2:S))) -> U21#(isList(V1:S),V2:S)
 ACTIVE(isList(__(V1:S,V2:S))) -> ISLIST(V1:S)
 ACTIVE(isList(__(V1:S,V2:S))) -> MARK(U21(isList(V1:S),V2:S))
 ACTIVE(isList(nil)) -> MARK(tt)
 ACTIVE(isList(V:S)) -> U11#(isNeList(V:S))
 ACTIVE(isList(V:S)) -> ISNELIST(V:S)
 ACTIVE(isList(V:S)) -> MARK(U11(isNeList(V:S)))
 ACTIVE(isNeList(__(V1:S,V2:S))) -> U41#(isList(V1:S),V2:S)
 ACTIVE(isNeList(__(V1:S,V2:S))) -> U51#(isNeList(V1:S),V2:S)
 ACTIVE(isNeList(__(V1:S,V2:S))) -> ISLIST(V1:S)
 ACTIVE(isNeList(__(V1:S,V2:S))) -> ISNELIST(V1:S)
 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U41(isList(V1:S),V2:S))
 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U51(isNeList(V1:S),V2:S))
 ACTIVE(isNeList(V:S)) -> U31#(isQid(V:S))
 ACTIVE(isNeList(V:S)) -> ISQID(V:S)
 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S)))
 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> U71#(isQid(I:S),P:S)
 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> ISQID(I:S)
 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S))
 ACTIVE(isNePal(V:S)) -> U61#(isQid(V:S))
 ACTIVE(isNePal(V:S)) -> ISQID(V:S)
 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S)))
 ACTIVE(isPal(nil)) -> MARK(tt)
 ACTIVE(isPal(V:S)) -> U81#(isNePal(V:S))
 ACTIVE(isPal(V:S)) -> ISNEPAL(V:S)
 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S)))
 ACTIVE(isQid(a)) -> MARK(tt)
 ACTIVE(isQid(e)) -> MARK(tt)
 ACTIVE(isQid(i)) -> MARK(tt)
 ACTIVE(isQid(o)) -> MARK(tt)
 ACTIVE(isQid(u)) -> MARK(tt)
 ISLIST(active(X:S)) -> ISLIST(X:S)
 ISLIST(mark(X:S)) -> ISLIST(X:S)
 ISNELIST(active(X:S)) -> ISNELIST(X:S)
 ISNELIST(mark(X:S)) -> ISNELIST(X:S)
 ISNEPAL(active(X:S)) -> ISNEPAL(X:S)
 ISNEPAL(mark(X:S)) -> ISNEPAL(X:S)
 ISPAL(active(X:S)) -> ISPAL(X:S)
 ISPAL(mark(X:S)) -> ISPAL(X:S)
 ISQID(active(X:S)) -> ISQID(X:S)
 ISQID(mark(X:S)) -> ISQID(X:S)
 MARK(U11(X:S)) -> U11#(mark(X:S))
 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S)))
 MARK(U11(X:S)) -> MARK(X:S)
 MARK(U21(X1:S,X2:S)) -> U21#(mark(X1:S),X2:S)
 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S))
 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U22(X:S)) -> U22#(mark(X:S))
 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S)))
 MARK(U22(X:S)) -> MARK(X:S)
 MARK(U31(X:S)) -> U31#(mark(X:S))
 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S)))
 MARK(U31(X:S)) -> MARK(X:S)
 MARK(U41(X1:S,X2:S)) -> U41#(mark(X1:S),X2:S)
 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S))
 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U42(X:S)) -> U42#(mark(X:S))
 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S)))
 MARK(U42(X:S)) -> MARK(X:S)
 MARK(U51(X1:S,X2:S)) -> U51#(mark(X1:S),X2:S)
 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S))
 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U52(X:S)) -> U52#(mark(X:S))
 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S)))
 MARK(U52(X:S)) -> MARK(X:S)
 MARK(U61(X:S)) -> U61#(mark(X:S))
 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S)))
 MARK(U61(X:S)) -> MARK(X:S)
 MARK(U71(X1:S,X2:S)) -> U71#(mark(X1:S),X2:S)
 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S))
 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U72(X:S)) -> U72#(mark(X:S))
 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S)))
 MARK(U72(X:S)) -> MARK(X:S)
 MARK(U81(X:S)) -> U81#(mark(X:S))
 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S)))
 MARK(U81(X:S)) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> __#(mark(X1:S),mark(X2:S))
 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(isList(X:S)) -> ACTIVE(isList(X:S))
 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S))
 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
 MARK(isQid(X:S)) -> ACTIVE(isQid(X:S))
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)

Problem 1: 

SCC Processor:
-> Pairs:
 U11#(active(X:S)) -> U11#(X:S)
 U11#(mark(X:S)) -> U11#(X:S)
 U21#(active(X1:S),X2:S) -> U21#(X1:S,X2:S)
 U21#(mark(X1:S),X2:S) -> U21#(X1:S,X2:S)
 U21#(X1:S,active(X2:S)) -> U21#(X1:S,X2:S)
 U21#(X1:S,mark(X2:S)) -> U21#(X1:S,X2:S)
 U22#(active(X:S)) -> U22#(X:S)
 U22#(mark(X:S)) -> U22#(X:S)
 U31#(active(X:S)) -> U31#(X:S)
 U31#(mark(X:S)) -> U31#(X:S)
 U41#(active(X1:S),X2:S) -> U41#(X1:S,X2:S)
 U41#(mark(X1:S),X2:S) -> U41#(X1:S,X2:S)
 U41#(X1:S,active(X2:S)) -> U41#(X1:S,X2:S)
 U41#(X1:S,mark(X2:S)) -> U41#(X1:S,X2:S)
 U42#(active(X:S)) -> U42#(X:S)
 U42#(mark(X:S)) -> U42#(X:S)
 U51#(active(X1:S),X2:S) -> U51#(X1:S,X2:S)
 U51#(mark(X1:S),X2:S) -> U51#(X1:S,X2:S)
 U51#(X1:S,active(X2:S)) -> U51#(X1:S,X2:S)
 U51#(X1:S,mark(X2:S)) -> U51#(X1:S,X2:S)
 U52#(active(X:S)) -> U52#(X:S)
 U52#(mark(X:S)) -> U52#(X:S)
 U61#(active(X:S)) -> U61#(X:S)
 U61#(mark(X:S)) -> U61#(X:S)
 U71#(active(X1:S),X2:S) -> U71#(X1:S,X2:S)
 U71#(mark(X1:S),X2:S) -> U71#(X1:S,X2:S)
 U71#(X1:S,active(X2:S)) -> U71#(X1:S,X2:S)
 U71#(X1:S,mark(X2:S)) -> U71#(X1:S,X2:S)
 U72#(active(X:S)) -> U72#(X:S)
 U72#(mark(X:S)) -> U72#(X:S)
 U81#(active(X:S)) -> U81#(X:S)
 U81#(mark(X:S)) -> U81#(X:S)
 __#(active(X1:S),X2:S) -> __#(X1:S,X2:S)
 __#(mark(X1:S),X2:S) -> __#(X1:S,X2:S)
 __#(X1:S,active(X2:S)) -> __#(X1:S,X2:S)
 __#(X1:S,mark(X2:S)) -> __#(X1:S,X2:S)
 ACTIVE(U11(tt)) -> MARK(tt)
 ACTIVE(U21(tt,V2:S)) -> U22#(isList(V2:S))
 ACTIVE(U21(tt,V2:S)) -> ISLIST(V2:S)
 ACTIVE(U21(tt,V2:S)) -> MARK(U22(isList(V2:S)))
 ACTIVE(U22(tt)) -> MARK(tt)
 ACTIVE(U31(tt)) -> MARK(tt)
 ACTIVE(U41(tt,V2:S)) -> U42#(isNeList(V2:S))
 ACTIVE(U41(tt,V2:S)) -> ISNELIST(V2:S)
 ACTIVE(U41(tt,V2:S)) -> MARK(U42(isNeList(V2:S)))
 ACTIVE(U42(tt)) -> MARK(tt)
 ACTIVE(U51(tt,V2:S)) -> U52#(isList(V2:S))
 ACTIVE(U51(tt,V2:S)) -> ISLIST(V2:S)
 ACTIVE(U51(tt,V2:S)) -> MARK(U52(isList(V2:S)))
 ACTIVE(U52(tt)) -> MARK(tt)
 ACTIVE(U61(tt)) -> MARK(tt)
 ACTIVE(U71(tt,P:S)) -> U72#(isPal(P:S))
 ACTIVE(U71(tt,P:S)) -> ISPAL(P:S)
 ACTIVE(U71(tt,P:S)) -> MARK(U72(isPal(P:S)))
 ACTIVE(U72(tt)) -> MARK(tt)
 ACTIVE(U81(tt)) -> MARK(tt)
 ACTIVE(__(__(X:S,Y:S),Z:S)) -> __#(X:S,__(Y:S,Z:S))
 ACTIVE(__(__(X:S,Y:S),Z:S)) -> __#(Y:S,Z:S)
 ACTIVE(__(__(X:S,Y:S),Z:S)) -> MARK(__(X:S,__(Y:S,Z:S)))
 ACTIVE(__(nil,X:S)) -> MARK(X:S)
 ACTIVE(__(X:S,nil)) -> MARK(X:S)
 ACTIVE(isList(__(V1:S,V2:S))) -> U21#(isList(V1:S),V2:S)
 ACTIVE(isList(__(V1:S,V2:S))) -> ISLIST(V1:S)
 ACTIVE(isList(__(V1:S,V2:S))) -> MARK(U21(isList(V1:S),V2:S))
 ACTIVE(isList(nil)) -> MARK(tt)
 ACTIVE(isList(V:S)) -> U11#(isNeList(V:S))
 ACTIVE(isList(V:S)) -> ISNELIST(V:S)
 ACTIVE(isList(V:S)) -> MARK(U11(isNeList(V:S)))
 ACTIVE(isNeList(__(V1:S,V2:S))) -> U41#(isList(V1:S),V2:S)
 ACTIVE(isNeList(__(V1:S,V2:S))) -> U51#(isNeList(V1:S),V2:S)
 ACTIVE(isNeList(__(V1:S,V2:S))) -> ISLIST(V1:S)
 ACTIVE(isNeList(__(V1:S,V2:S))) -> ISNELIST(V1:S)
 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U41(isList(V1:S),V2:S))
 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U51(isNeList(V1:S),V2:S))
 ACTIVE(isNeList(V:S)) -> U31#(isQid(V:S))
 ACTIVE(isNeList(V:S)) -> ISQID(V:S)
 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S)))
 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> U71#(isQid(I:S),P:S)
 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> ISQID(I:S)
 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S))
 ACTIVE(isNePal(V:S)) -> U61#(isQid(V:S))
 ACTIVE(isNePal(V:S)) -> ISQID(V:S)
 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S)))
 ACTIVE(isPal(nil)) -> MARK(tt)
 ACTIVE(isPal(V:S)) -> U81#(isNePal(V:S))
 ACTIVE(isPal(V:S)) -> ISNEPAL(V:S)
 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S)))
 ACTIVE(isQid(a)) -> MARK(tt)
 ACTIVE(isQid(e)) -> MARK(tt)
 ACTIVE(isQid(i)) -> MARK(tt)
 ACTIVE(isQid(o)) -> MARK(tt)
 ACTIVE(isQid(u)) -> MARK(tt)
 ISLIST(active(X:S)) -> ISLIST(X:S)
 ISLIST(mark(X:S)) -> ISLIST(X:S)
 ISNELIST(active(X:S)) -> ISNELIST(X:S)
 ISNELIST(mark(X:S)) -> ISNELIST(X:S)
 ISNEPAL(active(X:S)) -> ISNEPAL(X:S)
 ISNEPAL(mark(X:S)) -> ISNEPAL(X:S)
 ISPAL(active(X:S)) -> ISPAL(X:S)
 ISPAL(mark(X:S)) -> ISPAL(X:S)
 ISQID(active(X:S)) -> ISQID(X:S)
 ISQID(mark(X:S)) -> ISQID(X:S)
 MARK(U11(X:S)) -> U11#(mark(X:S))
 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S)))
 MARK(U11(X:S)) -> MARK(X:S)
 MARK(U21(X1:S,X2:S)) -> U21#(mark(X1:S),X2:S)
 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S))
 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U22(X:S)) -> U22#(mark(X:S))
 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S)))
 MARK(U22(X:S)) -> MARK(X:S)
 MARK(U31(X:S)) -> U31#(mark(X:S))
 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S)))
 MARK(U31(X:S)) -> MARK(X:S)
 MARK(U41(X1:S,X2:S)) -> U41#(mark(X1:S),X2:S)
 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S))
 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U42(X:S)) -> U42#(mark(X:S))
 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S)))
 MARK(U42(X:S)) -> MARK(X:S)
 MARK(U51(X1:S,X2:S)) -> U51#(mark(X1:S),X2:S)
 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S))
 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U52(X:S)) -> U52#(mark(X:S))
 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S)))
 MARK(U52(X:S)) -> MARK(X:S)
 MARK(U61(X:S)) -> U61#(mark(X:S))
 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S)))
 MARK(U61(X:S)) -> MARK(X:S)
 MARK(U71(X1:S,X2:S)) -> U71#(mark(X1:S),X2:S)
 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S))
 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U72(X:S)) -> U72#(mark(X:S))
 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S)))
 MARK(U72(X:S)) -> MARK(X:S)
 MARK(U81(X:S)) -> U81#(mark(X:S))
 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S)))
 MARK(U81(X:S)) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> __#(mark(X1:S),mark(X2:S))
 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(isList(X:S)) -> ACTIVE(isList(X:S))
 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S))
 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
 MARK(isQid(X:S)) -> ACTIVE(isQid(X:S))
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ISQID(active(X:S)) -> ISQID(X:S)
 ISQID(mark(X:S)) -> ISQID(X:S)
->->-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->->Cycle:
->->-> Pairs:
 ISPAL(active(X:S)) -> ISPAL(X:S)
 ISPAL(mark(X:S)) -> ISPAL(X:S)
->->-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->->Cycle:
->->-> Pairs:
 ISNEPAL(active(X:S)) -> ISNEPAL(X:S)
 ISNEPAL(mark(X:S)) -> ISNEPAL(X:S)
->->-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->->Cycle:
->->-> Pairs:
 ISNELIST(active(X:S)) -> ISNELIST(X:S)
 ISNELIST(mark(X:S)) -> ISNELIST(X:S)
->->-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->->Cycle:
->->-> Pairs:
 ISLIST(active(X:S)) -> ISLIST(X:S)
 ISLIST(mark(X:S)) -> ISLIST(X:S)
->->-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->->Cycle:
->->-> Pairs:
 __#(active(X1:S),X2:S) -> __#(X1:S,X2:S)
 __#(mark(X1:S),X2:S) -> __#(X1:S,X2:S)
 __#(X1:S,active(X2:S)) -> __#(X1:S,X2:S)
 __#(X1:S,mark(X2:S)) -> __#(X1:S,X2:S)
->->-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->->Cycle:
->->-> Pairs:
 U81#(active(X:S)) -> U81#(X:S)
 U81#(mark(X:S)) -> U81#(X:S)
->->-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->->Cycle:
->->-> Pairs:
 U72#(active(X:S)) -> U72#(X:S)
 U72#(mark(X:S)) -> U72#(X:S)
->->-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->->Cycle:
->->-> Pairs:
 U71#(active(X1:S),X2:S) -> U71#(X1:S,X2:S)
 U71#(mark(X1:S),X2:S) -> U71#(X1:S,X2:S)
 U71#(X1:S,active(X2:S)) -> U71#(X1:S,X2:S)
 U71#(X1:S,mark(X2:S)) -> U71#(X1:S,X2:S)
->->-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->->Cycle:
->->-> Pairs:
 U61#(active(X:S)) -> U61#(X:S)
 U61#(mark(X:S)) -> U61#(X:S)
->->-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->->Cycle:
->->-> Pairs:
 U52#(active(X:S)) -> U52#(X:S)
 U52#(mark(X:S)) -> U52#(X:S)
->->-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->->Cycle:
->->-> Pairs:
 U51#(active(X1:S),X2:S) -> U51#(X1:S,X2:S)
 U51#(mark(X1:S),X2:S) -> U51#(X1:S,X2:S)
 U51#(X1:S,active(X2:S)) -> U51#(X1:S,X2:S)
 U51#(X1:S,mark(X2:S)) -> U51#(X1:S,X2:S)
->->-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->->Cycle:
->->-> Pairs:
 U42#(active(X:S)) -> U42#(X:S)
 U42#(mark(X:S)) -> U42#(X:S)
->->-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->->Cycle:
->->-> Pairs:
 U41#(active(X1:S),X2:S) -> U41#(X1:S,X2:S)
 U41#(mark(X1:S),X2:S) -> U41#(X1:S,X2:S)
 U41#(X1:S,active(X2:S)) -> U41#(X1:S,X2:S)
 U41#(X1:S,mark(X2:S)) -> U41#(X1:S,X2:S)
->->-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->->Cycle:
->->-> Pairs:
 U31#(active(X:S)) -> U31#(X:S)
 U31#(mark(X:S)) -> U31#(X:S)
->->-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->->Cycle:
->->-> Pairs:
 U22#(active(X:S)) -> U22#(X:S)
 U22#(mark(X:S)) -> U22#(X:S)
->->-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->->Cycle:
->->-> Pairs:
 U21#(active(X1:S),X2:S) -> U21#(X1:S,X2:S)
 U21#(mark(X1:S),X2:S) -> U21#(X1:S,X2:S)
 U21#(X1:S,active(X2:S)) -> U21#(X1:S,X2:S)
 U21#(X1:S,mark(X2:S)) -> U21#(X1:S,X2:S)
->->-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->->Cycle:
->->-> Pairs:
 U11#(active(X:S)) -> U11#(X:S)
 U11#(mark(X:S)) -> U11#(X:S)
->->-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->->Cycle:
->->-> Pairs:
 ACTIVE(U21(tt,V2:S)) -> MARK(U22(isList(V2:S)))
 ACTIVE(U41(tt,V2:S)) -> MARK(U42(isNeList(V2:S)))
 ACTIVE(U51(tt,V2:S)) -> MARK(U52(isList(V2:S)))
 ACTIVE(U71(tt,P:S)) -> MARK(U72(isPal(P:S)))
 ACTIVE(__(__(X:S,Y:S),Z:S)) -> MARK(__(X:S,__(Y:S,Z:S)))
 ACTIVE(__(nil,X:S)) -> MARK(X:S)
 ACTIVE(__(X:S,nil)) -> MARK(X:S)
 ACTIVE(isList(__(V1:S,V2:S))) -> MARK(U21(isList(V1:S),V2:S))
 ACTIVE(isList(V:S)) -> MARK(U11(isNeList(V:S)))
 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U41(isList(V1:S),V2:S))
 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U51(isNeList(V1:S),V2:S))
 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S)))
 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S))
 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S)))
 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S)))
 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S)))
 MARK(U11(X:S)) -> MARK(X:S)
 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S))
 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S)))
 MARK(U22(X:S)) -> MARK(X:S)
 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S)))
 MARK(U31(X:S)) -> MARK(X:S)
 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S))
 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S)))
 MARK(U42(X:S)) -> MARK(X:S)
 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S))
 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S)))
 MARK(U52(X:S)) -> MARK(X:S)
 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S)))
 MARK(U61(X:S)) -> MARK(X:S)
 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S))
 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S)))
 MARK(U72(X:S)) -> MARK(X:S)
 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S)))
 MARK(U81(X:S)) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(isList(X:S)) -> ACTIVE(isList(X:S))
 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S))
 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
->->-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)


The problem is decomposed in 19 subproblems.

Problem 1.1: 

Subterm Processor:
-> Pairs:
 ISQID(active(X:S)) -> ISQID(X:S)
 ISQID(mark(X:S)) -> ISQID(X:S)
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Projection:
 pi(ISQID) = 1

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

Subterm Processor:
-> Pairs:
 ISPAL(active(X:S)) -> ISPAL(X:S)
 ISPAL(mark(X:S)) -> ISPAL(X:S)
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Projection:
 pi(ISPAL) = 1

Problem 1.2: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.3: 

Subterm Processor:
-> Pairs:
 ISNEPAL(active(X:S)) -> ISNEPAL(X:S)
 ISNEPAL(mark(X:S)) -> ISNEPAL(X:S)
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Projection:
 pi(ISNEPAL) = 1

Problem 1.3: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.4: 

Subterm Processor:
-> Pairs:
 ISNELIST(active(X:S)) -> ISNELIST(X:S)
 ISNELIST(mark(X:S)) -> ISNELIST(X:S)
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Projection:
 pi(ISNELIST) = 1

Problem 1.4: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.5: 

Subterm Processor:
-> Pairs:
 ISLIST(active(X:S)) -> ISLIST(X:S)
 ISLIST(mark(X:S)) -> ISLIST(X:S)
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Projection:
 pi(ISLIST) = 1

Problem 1.5: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.6: 

Subterm Processor:
-> Pairs:
 __#(active(X1:S),X2:S) -> __#(X1:S,X2:S)
 __#(mark(X1:S),X2:S) -> __#(X1:S,X2:S)
 __#(X1:S,active(X2:S)) -> __#(X1:S,X2:S)
 __#(X1:S,mark(X2:S)) -> __#(X1:S,X2:S)
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Projection:
 pi(__#) = 1

Problem 1.6: 

SCC Processor:
-> Pairs:
 __#(X1:S,active(X2:S)) -> __#(X1:S,X2:S)
 __#(X1:S,mark(X2:S)) -> __#(X1:S,X2:S)
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 __#(X1:S,active(X2:S)) -> __#(X1:S,X2:S)
 __#(X1:S,mark(X2:S)) -> __#(X1:S,X2:S)
->->-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)

Problem 1.6: 

Subterm Processor:
-> Pairs:
 __#(X1:S,active(X2:S)) -> __#(X1:S,X2:S)
 __#(X1:S,mark(X2:S)) -> __#(X1:S,X2:S)
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Projection:
 pi(__#) = 2

Problem 1.6: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.7: 

Subterm Processor:
-> Pairs:
 U81#(active(X:S)) -> U81#(X:S)
 U81#(mark(X:S)) -> U81#(X:S)
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Projection:
 pi(U81#) = 1

Problem 1.7: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.8: 

Subterm Processor:
-> Pairs:
 U72#(active(X:S)) -> U72#(X:S)
 U72#(mark(X:S)) -> U72#(X:S)
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Projection:
 pi(U72#) = 1

Problem 1.8: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.9: 

Subterm Processor:
-> Pairs:
 U71#(active(X1:S),X2:S) -> U71#(X1:S,X2:S)
 U71#(mark(X1:S),X2:S) -> U71#(X1:S,X2:S)
 U71#(X1:S,active(X2:S)) -> U71#(X1:S,X2:S)
 U71#(X1:S,mark(X2:S)) -> U71#(X1:S,X2:S)
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Projection:
 pi(U71#) = 1

Problem 1.9: 

SCC Processor:
-> Pairs:
 U71#(X1:S,active(X2:S)) -> U71#(X1:S,X2:S)
 U71#(X1:S,mark(X2:S)) -> U71#(X1:S,X2:S)
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 U71#(X1:S,active(X2:S)) -> U71#(X1:S,X2:S)
 U71#(X1:S,mark(X2:S)) -> U71#(X1:S,X2:S)
->->-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)

Problem 1.9: 

Subterm Processor:
-> Pairs:
 U71#(X1:S,active(X2:S)) -> U71#(X1:S,X2:S)
 U71#(X1:S,mark(X2:S)) -> U71#(X1:S,X2:S)
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Projection:
 pi(U71#) = 2

Problem 1.9: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.10: 

Subterm Processor:
-> Pairs:
 U61#(active(X:S)) -> U61#(X:S)
 U61#(mark(X:S)) -> U61#(X:S)
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Projection:
 pi(U61#) = 1

Problem 1.10: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.11: 

Subterm Processor:
-> Pairs:
 U52#(active(X:S)) -> U52#(X:S)
 U52#(mark(X:S)) -> U52#(X:S)
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Projection:
 pi(U52#) = 1

Problem 1.11: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.12: 

Subterm Processor:
-> Pairs:
 U51#(active(X1:S),X2:S) -> U51#(X1:S,X2:S)
 U51#(mark(X1:S),X2:S) -> U51#(X1:S,X2:S)
 U51#(X1:S,active(X2:S)) -> U51#(X1:S,X2:S)
 U51#(X1:S,mark(X2:S)) -> U51#(X1:S,X2:S)
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Projection:
 pi(U51#) = 1

Problem 1.12: 

SCC Processor:
-> Pairs:
 U51#(X1:S,active(X2:S)) -> U51#(X1:S,X2:S)
 U51#(X1:S,mark(X2:S)) -> U51#(X1:S,X2:S)
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 U51#(X1:S,active(X2:S)) -> U51#(X1:S,X2:S)
 U51#(X1:S,mark(X2:S)) -> U51#(X1:S,X2:S)
->->-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)

Problem 1.12: 

Subterm Processor:
-> Pairs:
 U51#(X1:S,active(X2:S)) -> U51#(X1:S,X2:S)
 U51#(X1:S,mark(X2:S)) -> U51#(X1:S,X2:S)
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Projection:
 pi(U51#) = 2

Problem 1.12: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.13: 

Subterm Processor:
-> Pairs:
 U42#(active(X:S)) -> U42#(X:S)
 U42#(mark(X:S)) -> U42#(X:S)
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Projection:
 pi(U42#) = 1

Problem 1.13: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.14: 

Subterm Processor:
-> Pairs:
 U41#(active(X1:S),X2:S) -> U41#(X1:S,X2:S)
 U41#(mark(X1:S),X2:S) -> U41#(X1:S,X2:S)
 U41#(X1:S,active(X2:S)) -> U41#(X1:S,X2:S)
 U41#(X1:S,mark(X2:S)) -> U41#(X1:S,X2:S)
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Projection:
 pi(U41#) = 1

Problem 1.14: 

SCC Processor:
-> Pairs:
 U41#(X1:S,active(X2:S)) -> U41#(X1:S,X2:S)
 U41#(X1:S,mark(X2:S)) -> U41#(X1:S,X2:S)
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 U41#(X1:S,active(X2:S)) -> U41#(X1:S,X2:S)
 U41#(X1:S,mark(X2:S)) -> U41#(X1:S,X2:S)
->->-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)

Problem 1.14: 

Subterm Processor:
-> Pairs:
 U41#(X1:S,active(X2:S)) -> U41#(X1:S,X2:S)
 U41#(X1:S,mark(X2:S)) -> U41#(X1:S,X2:S)
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Projection:
 pi(U41#) = 2

Problem 1.14: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.15: 

Subterm Processor:
-> Pairs:
 U31#(active(X:S)) -> U31#(X:S)
 U31#(mark(X:S)) -> U31#(X:S)
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Projection:
 pi(U31#) = 1

Problem 1.15: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.16: 

Subterm Processor:
-> Pairs:
 U22#(active(X:S)) -> U22#(X:S)
 U22#(mark(X:S)) -> U22#(X:S)
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Projection:
 pi(U22#) = 1

Problem 1.16: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.17: 

Subterm Processor:
-> Pairs:
 U21#(active(X1:S),X2:S) -> U21#(X1:S,X2:S)
 U21#(mark(X1:S),X2:S) -> U21#(X1:S,X2:S)
 U21#(X1:S,active(X2:S)) -> U21#(X1:S,X2:S)
 U21#(X1:S,mark(X2:S)) -> U21#(X1:S,X2:S)
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Projection:
 pi(U21#) = 1

Problem 1.17: 

SCC Processor:
-> Pairs:
 U21#(X1:S,active(X2:S)) -> U21#(X1:S,X2:S)
 U21#(X1:S,mark(X2:S)) -> U21#(X1:S,X2:S)
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 U21#(X1:S,active(X2:S)) -> U21#(X1:S,X2:S)
 U21#(X1:S,mark(X2:S)) -> U21#(X1:S,X2:S)
->->-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)

Problem 1.17: 

Subterm Processor:
-> Pairs:
 U21#(X1:S,active(X2:S)) -> U21#(X1:S,X2:S)
 U21#(X1:S,mark(X2:S)) -> U21#(X1:S,X2:S)
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Projection:
 pi(U21#) = 2

Problem 1.17: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.18: 

Subterm Processor:
-> Pairs:
 U11#(active(X:S)) -> U11#(X:S)
 U11#(mark(X:S)) -> U11#(X:S)
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Projection:
 pi(U11#) = 1

Problem 1.18: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.19: 

Reduction Pairs Processor:
-> Pairs:
 ACTIVE(U21(tt,V2:S)) -> MARK(U22(isList(V2:S)))
 ACTIVE(U41(tt,V2:S)) -> MARK(U42(isNeList(V2:S)))
 ACTIVE(U51(tt,V2:S)) -> MARK(U52(isList(V2:S)))
 ACTIVE(U71(tt,P:S)) -> MARK(U72(isPal(P:S)))
 ACTIVE(__(__(X:S,Y:S),Z:S)) -> MARK(__(X:S,__(Y:S,Z:S)))
 ACTIVE(__(nil,X:S)) -> MARK(X:S)
 ACTIVE(__(X:S,nil)) -> MARK(X:S)
 ACTIVE(isList(__(V1:S,V2:S))) -> MARK(U21(isList(V1:S),V2:S))
 ACTIVE(isList(V:S)) -> MARK(U11(isNeList(V:S)))
 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U41(isList(V1:S),V2:S))
 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U51(isNeList(V1:S),V2:S))
 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S)))
 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S))
 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S)))
 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S)))
 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S)))
 MARK(U11(X:S)) -> MARK(X:S)
 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S))
 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S)))
 MARK(U22(X:S)) -> MARK(X:S)
 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S)))
 MARK(U31(X:S)) -> MARK(X:S)
 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S))
 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S)))
 MARK(U42(X:S)) -> MARK(X:S)
 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S))
 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S)))
 MARK(U52(X:S)) -> MARK(X:S)
 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S)))
 MARK(U61(X:S)) -> MARK(X:S)
 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S))
 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S)))
 MARK(U72(X:S)) -> MARK(X:S)
 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S)))
 MARK(U81(X:S)) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(isList(X:S)) -> ACTIVE(isList(X:S))
 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S))
 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
-> Usable rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[U11](X) = X
[U21](X1,X2) = 2.X1 + 2.X2 + 2
[U22](X) = X + 2
[U31](X) = X
[U41](X1,X2) = 2.X1 + 2.X2 + 1
[U42](X) = X
[U51](X1,X2) = X1 + 2.X2 + 2
[U52](X) = X + 1
[U61](X) = X
[U71](X1,X2) = 2.X1 + 2.X2 + 2
[U72](X) = X + 2
[U81](X) = X
[__](X1,X2) = 2.X1 + X2 + 2
[active](X) = X
[isList](X) = 2.X + 2
[isNeList](X) = 2.X + 2
[isNePal](X) = 2.X + 2
[isPal](X) = 2.X + 2
[isQid](X) = 2.X + 2
[mark](X) = X
[a] = 2
[e] = 2
[fSNonEmpty] = 0
[i] = 2
[nil] = 1
[o] = 2
[tt] = 2
[u] = 1
[U11#](X) = 0
[U21#](X1,X2) = 0
[U22#](X) = 0
[U31#](X) = 0
[U41#](X1,X2) = 0
[U42#](X) = 0
[U51#](X1,X2) = 0
[U52#](X) = 0
[U61#](X) = 0
[U71#](X1,X2) = 0
[U72#](X) = 0
[U81#](X) = 0
[__#](X1,X2) = 0
[ACTIVE](X) = 2.X + 2
[ISLIST](X) = 0
[ISNELIST](X) = 0
[ISNEPAL](X) = 0
[ISPAL](X) = 0
[ISQID](X) = 0
[MARK](X) = 2.X + 2

Problem 1.19: 

SCC Processor:
-> Pairs:
 ACTIVE(U41(tt,V2:S)) -> MARK(U42(isNeList(V2:S)))
 ACTIVE(U51(tt,V2:S)) -> MARK(U52(isList(V2:S)))
 ACTIVE(U71(tt,P:S)) -> MARK(U72(isPal(P:S)))
 ACTIVE(__(__(X:S,Y:S),Z:S)) -> MARK(__(X:S,__(Y:S,Z:S)))
 ACTIVE(__(nil,X:S)) -> MARK(X:S)
 ACTIVE(__(X:S,nil)) -> MARK(X:S)
 ACTIVE(isList(__(V1:S,V2:S))) -> MARK(U21(isList(V1:S),V2:S))
 ACTIVE(isList(V:S)) -> MARK(U11(isNeList(V:S)))
 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U41(isList(V1:S),V2:S))
 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U51(isNeList(V1:S),V2:S))
 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S)))
 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S))
 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S)))
 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S)))
 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S)))
 MARK(U11(X:S)) -> MARK(X:S)
 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S))
 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S)))
 MARK(U22(X:S)) -> MARK(X:S)
 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S)))
 MARK(U31(X:S)) -> MARK(X:S)
 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S))
 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S)))
 MARK(U42(X:S)) -> MARK(X:S)
 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S))
 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S)))
 MARK(U52(X:S)) -> MARK(X:S)
 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S)))
 MARK(U61(X:S)) -> MARK(X:S)
 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S))
 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S)))
 MARK(U72(X:S)) -> MARK(X:S)
 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S)))
 MARK(U81(X:S)) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(isList(X:S)) -> ACTIVE(isList(X:S))
 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S))
 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ACTIVE(U41(tt,V2:S)) -> MARK(U42(isNeList(V2:S)))
 ACTIVE(U51(tt,V2:S)) -> MARK(U52(isList(V2:S)))
 ACTIVE(U71(tt,P:S)) -> MARK(U72(isPal(P:S)))
 ACTIVE(__(__(X:S,Y:S),Z:S)) -> MARK(__(X:S,__(Y:S,Z:S)))
 ACTIVE(__(nil,X:S)) -> MARK(X:S)
 ACTIVE(__(X:S,nil)) -> MARK(X:S)
 ACTIVE(isList(__(V1:S,V2:S))) -> MARK(U21(isList(V1:S),V2:S))
 ACTIVE(isList(V:S)) -> MARK(U11(isNeList(V:S)))
 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U41(isList(V1:S),V2:S))
 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U51(isNeList(V1:S),V2:S))
 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S)))
 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S))
 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S)))
 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S)))
 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S)))
 MARK(U11(X:S)) -> MARK(X:S)
 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S))
 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S)))
 MARK(U22(X:S)) -> MARK(X:S)
 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S)))
 MARK(U31(X:S)) -> MARK(X:S)
 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S))
 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S)))
 MARK(U42(X:S)) -> MARK(X:S)
 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S))
 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S)))
 MARK(U52(X:S)) -> MARK(X:S)
 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S)))
 MARK(U61(X:S)) -> MARK(X:S)
 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S))
 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S)))
 MARK(U72(X:S)) -> MARK(X:S)
 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S)))
 MARK(U81(X:S)) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(isList(X:S)) -> ACTIVE(isList(X:S))
 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S))
 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
->->-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)

Problem 1.19: 

Reduction Pairs Processor:
-> Pairs:
 ACTIVE(U41(tt,V2:S)) -> MARK(U42(isNeList(V2:S)))
 ACTIVE(U51(tt,V2:S)) -> MARK(U52(isList(V2:S)))
 ACTIVE(U71(tt,P:S)) -> MARK(U72(isPal(P:S)))
 ACTIVE(__(__(X:S,Y:S),Z:S)) -> MARK(__(X:S,__(Y:S,Z:S)))
 ACTIVE(__(nil,X:S)) -> MARK(X:S)
 ACTIVE(__(X:S,nil)) -> MARK(X:S)
 ACTIVE(isList(__(V1:S,V2:S))) -> MARK(U21(isList(V1:S),V2:S))
 ACTIVE(isList(V:S)) -> MARK(U11(isNeList(V:S)))
 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U41(isList(V1:S),V2:S))
 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U51(isNeList(V1:S),V2:S))
 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S)))
 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S))
 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S)))
 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S)))
 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S)))
 MARK(U11(X:S)) -> MARK(X:S)
 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S))
 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S)))
 MARK(U22(X:S)) -> MARK(X:S)
 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S)))
 MARK(U31(X:S)) -> MARK(X:S)
 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S))
 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S)))
 MARK(U42(X:S)) -> MARK(X:S)
 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S))
 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S)))
 MARK(U52(X:S)) -> MARK(X:S)
 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S)))
 MARK(U61(X:S)) -> MARK(X:S)
 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S))
 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S)))
 MARK(U72(X:S)) -> MARK(X:S)
 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S)))
 MARK(U81(X:S)) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(isList(X:S)) -> ACTIVE(isList(X:S))
 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S))
 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
-> Usable rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[U11](X) = X
[U21](X1,X2) = X1 + 2.X2 + 2
[U22](X) = X
[U31](X) = X + 1
[U41](X1,X2) = 2.X1 + 2.X2 + 2
[U42](X) = X
[U51](X1,X2) = 2.X1 + 2.X2 + 2
[U52](X) = X + 2
[U61](X) = X + 1
[U71](X1,X2) = 2.X1 + 2.X2
[U72](X) = X + 2
[U81](X) = X
[__](X1,X2) = 2.X1 + X2 + 2
[active](X) = X
[isList](X) = 2.X + 2
[isNeList](X) = 2.X + 2
[isNePal](X) = 2.X + 2
[isPal](X) = 2.X + 2
[isQid](X) = 2.X + 1
[mark](X) = X
[a] = 2
[e] = 1
[fSNonEmpty] = 0
[i] = 1
[nil] = 0
[o] = 2
[tt] = 2
[u] = 2
[U11#](X) = 0
[U21#](X1,X2) = 0
[U22#](X) = 0
[U31#](X) = 0
[U41#](X1,X2) = 0
[U42#](X) = 0
[U51#](X1,X2) = 0
[U52#](X) = 0
[U61#](X) = 0
[U71#](X1,X2) = 0
[U72#](X) = 0
[U81#](X) = 0
[__#](X1,X2) = 0
[ACTIVE](X) = 2.X + 2
[ISLIST](X) = 0
[ISNELIST](X) = 0
[ISNEPAL](X) = 0
[ISPAL](X) = 0
[ISQID](X) = 0
[MARK](X) = 2.X + 2

Problem 1.19: 

SCC Processor:
-> Pairs:
 ACTIVE(U51(tt,V2:S)) -> MARK(U52(isList(V2:S)))
 ACTIVE(U71(tt,P:S)) -> MARK(U72(isPal(P:S)))
 ACTIVE(__(__(X:S,Y:S),Z:S)) -> MARK(__(X:S,__(Y:S,Z:S)))
 ACTIVE(__(nil,X:S)) -> MARK(X:S)
 ACTIVE(__(X:S,nil)) -> MARK(X:S)
 ACTIVE(isList(__(V1:S,V2:S))) -> MARK(U21(isList(V1:S),V2:S))
 ACTIVE(isList(V:S)) -> MARK(U11(isNeList(V:S)))
 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U41(isList(V1:S),V2:S))
 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U51(isNeList(V1:S),V2:S))
 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S)))
 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S))
 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S)))
 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S)))
 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S)))
 MARK(U11(X:S)) -> MARK(X:S)
 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S))
 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S)))
 MARK(U22(X:S)) -> MARK(X:S)
 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S)))
 MARK(U31(X:S)) -> MARK(X:S)
 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S))
 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S)))
 MARK(U42(X:S)) -> MARK(X:S)
 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S))
 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S)))
 MARK(U52(X:S)) -> MARK(X:S)
 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S)))
 MARK(U61(X:S)) -> MARK(X:S)
 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S))
 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S)))
 MARK(U72(X:S)) -> MARK(X:S)
 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S)))
 MARK(U81(X:S)) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(isList(X:S)) -> ACTIVE(isList(X:S))
 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S))
 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ACTIVE(U51(tt,V2:S)) -> MARK(U52(isList(V2:S)))
 ACTIVE(U71(tt,P:S)) -> MARK(U72(isPal(P:S)))
 ACTIVE(__(__(X:S,Y:S),Z:S)) -> MARK(__(X:S,__(Y:S,Z:S)))
 ACTIVE(__(nil,X:S)) -> MARK(X:S)
 ACTIVE(__(X:S,nil)) -> MARK(X:S)
 ACTIVE(isList(__(V1:S,V2:S))) -> MARK(U21(isList(V1:S),V2:S))
 ACTIVE(isList(V:S)) -> MARK(U11(isNeList(V:S)))
 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U41(isList(V1:S),V2:S))
 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U51(isNeList(V1:S),V2:S))
 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S)))
 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S))
 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S)))
 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S)))
 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S)))
 MARK(U11(X:S)) -> MARK(X:S)
 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S))
 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S)))
 MARK(U22(X:S)) -> MARK(X:S)
 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S)))
 MARK(U31(X:S)) -> MARK(X:S)
 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S))
 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S)))
 MARK(U42(X:S)) -> MARK(X:S)
 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S))
 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S)))
 MARK(U52(X:S)) -> MARK(X:S)
 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S)))
 MARK(U61(X:S)) -> MARK(X:S)
 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S))
 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S)))
 MARK(U72(X:S)) -> MARK(X:S)
 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S)))
 MARK(U81(X:S)) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(isList(X:S)) -> ACTIVE(isList(X:S))
 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S))
 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
->->-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)

Problem 1.19: 

Reduction Pairs Processor:
-> Pairs:
 ACTIVE(U51(tt,V2:S)) -> MARK(U52(isList(V2:S)))
 ACTIVE(U71(tt,P:S)) -> MARK(U72(isPal(P:S)))
 ACTIVE(__(__(X:S,Y:S),Z:S)) -> MARK(__(X:S,__(Y:S,Z:S)))
 ACTIVE(__(nil,X:S)) -> MARK(X:S)
 ACTIVE(__(X:S,nil)) -> MARK(X:S)
 ACTIVE(isList(__(V1:S,V2:S))) -> MARK(U21(isList(V1:S),V2:S))
 ACTIVE(isList(V:S)) -> MARK(U11(isNeList(V:S)))
 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U41(isList(V1:S),V2:S))
 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U51(isNeList(V1:S),V2:S))
 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S)))
 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S))
 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S)))
 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S)))
 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S)))
 MARK(U11(X:S)) -> MARK(X:S)
 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S))
 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S)))
 MARK(U22(X:S)) -> MARK(X:S)
 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S)))
 MARK(U31(X:S)) -> MARK(X:S)
 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S))
 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S)))
 MARK(U42(X:S)) -> MARK(X:S)
 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S))
 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S)))
 MARK(U52(X:S)) -> MARK(X:S)
 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S)))
 MARK(U61(X:S)) -> MARK(X:S)
 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S))
 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S)))
 MARK(U72(X:S)) -> MARK(X:S)
 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S)))
 MARK(U81(X:S)) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(isList(X:S)) -> ACTIVE(isList(X:S))
 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S))
 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
-> Usable rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[U11](X) = X
[U21](X1,X2) = 2.X1 + 2.X2 + 1
[U22](X) = X + 2
[U31](X) = 2.X
[U41](X1,X2) = 2.X1 + 2.X2 + 2
[U42](X) = X + 2
[U51](X1,X2) = 2.X1 + 2.X2 + 2
[U52](X) = X
[U61](X) = 2.X
[U71](X1,X2) = 2.X1 + 2.X2 + 2
[U72](X) = X + 2
[U81](X) = X
[__](X1,X2) = 2.X1 + X2 + 2
[active](X) = X
[isList](X) = 2.X + 2
[isNeList](X) = 2.X + 2
[isNePal](X) = 2.X + 2
[isPal](X) = 2.X + 2
[isQid](X) = X + 1
[mark](X) = X
[a] = 2
[e] = 2
[fSNonEmpty] = 0
[i] = 2
[nil] = 2
[o] = 2
[tt] = 2
[u] = 2
[U11#](X) = 0
[U21#](X1,X2) = 0
[U22#](X) = 0
[U31#](X) = 0
[U41#](X1,X2) = 0
[U42#](X) = 0
[U51#](X1,X2) = 0
[U52#](X) = 0
[U61#](X) = 0
[U71#](X1,X2) = 0
[U72#](X) = 0
[U81#](X) = 0
[__#](X1,X2) = 0
[ACTIVE](X) = 2.X + 2
[ISLIST](X) = 0
[ISNELIST](X) = 0
[ISNEPAL](X) = 0
[ISPAL](X) = 0
[ISQID](X) = 0
[MARK](X) = 2.X + 2

Problem 1.19: 

SCC Processor:
-> Pairs:
 ACTIVE(U71(tt,P:S)) -> MARK(U72(isPal(P:S)))
 ACTIVE(__(__(X:S,Y:S),Z:S)) -> MARK(__(X:S,__(Y:S,Z:S)))
 ACTIVE(__(nil,X:S)) -> MARK(X:S)
 ACTIVE(__(X:S,nil)) -> MARK(X:S)
 ACTIVE(isList(__(V1:S,V2:S))) -> MARK(U21(isList(V1:S),V2:S))
 ACTIVE(isList(V:S)) -> MARK(U11(isNeList(V:S)))
 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U41(isList(V1:S),V2:S))
 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U51(isNeList(V1:S),V2:S))
 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S)))
 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S))
 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S)))
 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S)))
 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S)))
 MARK(U11(X:S)) -> MARK(X:S)
 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S))
 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S)))
 MARK(U22(X:S)) -> MARK(X:S)
 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S)))
 MARK(U31(X:S)) -> MARK(X:S)
 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S))
 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S)))
 MARK(U42(X:S)) -> MARK(X:S)
 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S))
 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S)))
 MARK(U52(X:S)) -> MARK(X:S)
 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S)))
 MARK(U61(X:S)) -> MARK(X:S)
 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S))
 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S)))
 MARK(U72(X:S)) -> MARK(X:S)
 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S)))
 MARK(U81(X:S)) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(isList(X:S)) -> ACTIVE(isList(X:S))
 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S))
 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ACTIVE(U71(tt,P:S)) -> MARK(U72(isPal(P:S)))
 ACTIVE(__(__(X:S,Y:S),Z:S)) -> MARK(__(X:S,__(Y:S,Z:S)))
 ACTIVE(__(nil,X:S)) -> MARK(X:S)
 ACTIVE(__(X:S,nil)) -> MARK(X:S)
 ACTIVE(isList(__(V1:S,V2:S))) -> MARK(U21(isList(V1:S),V2:S))
 ACTIVE(isList(V:S)) -> MARK(U11(isNeList(V:S)))
 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U41(isList(V1:S),V2:S))
 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U51(isNeList(V1:S),V2:S))
 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S)))
 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S))
 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S)))
 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S)))
 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S)))
 MARK(U11(X:S)) -> MARK(X:S)
 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S))
 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S)))
 MARK(U22(X:S)) -> MARK(X:S)
 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S)))
 MARK(U31(X:S)) -> MARK(X:S)
 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S))
 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S)))
 MARK(U42(X:S)) -> MARK(X:S)
 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S))
 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S)))
 MARK(U52(X:S)) -> MARK(X:S)
 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S)))
 MARK(U61(X:S)) -> MARK(X:S)
 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S))
 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S)))
 MARK(U72(X:S)) -> MARK(X:S)
 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S)))
 MARK(U81(X:S)) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(isList(X:S)) -> ACTIVE(isList(X:S))
 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S))
 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
->->-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)

Problem 1.19: 

Reduction Pairs Processor:
-> Pairs:
 ACTIVE(U71(tt,P:S)) -> MARK(U72(isPal(P:S)))
 ACTIVE(__(__(X:S,Y:S),Z:S)) -> MARK(__(X:S,__(Y:S,Z:S)))
 ACTIVE(__(nil,X:S)) -> MARK(X:S)
 ACTIVE(__(X:S,nil)) -> MARK(X:S)
 ACTIVE(isList(__(V1:S,V2:S))) -> MARK(U21(isList(V1:S),V2:S))
 ACTIVE(isList(V:S)) -> MARK(U11(isNeList(V:S)))
 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U41(isList(V1:S),V2:S))
 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U51(isNeList(V1:S),V2:S))
 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S)))
 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S))
 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S)))
 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S)))
 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S)))
 MARK(U11(X:S)) -> MARK(X:S)
 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S))
 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S)))
 MARK(U22(X:S)) -> MARK(X:S)
 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S)))
 MARK(U31(X:S)) -> MARK(X:S)
 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S))
 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S)))
 MARK(U42(X:S)) -> MARK(X:S)
 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S))
 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S)))
 MARK(U52(X:S)) -> MARK(X:S)
 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S)))
 MARK(U61(X:S)) -> MARK(X:S)
 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S))
 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S)))
 MARK(U72(X:S)) -> MARK(X:S)
 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S)))
 MARK(U81(X:S)) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(isList(X:S)) -> ACTIVE(isList(X:S))
 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S))
 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
-> Usable rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[U11](X) = X
[U21](X1,X2) = X1 + 2.X2 + 2
[U22](X) = X + 1
[U31](X) = 2.X
[U41](X1,X2) = 2.X1 + 2.X2 + 2
[U42](X) = X + 2
[U51](X1,X2) = 2.X1 + 2.X2 + 2
[U52](X) = X + 1
[U61](X) = 2.X
[U71](X1,X2) = 2.X1 + 2.X2 + 2
[U72](X) = X + 2
[U81](X) = X
[__](X1,X2) = 2.X1 + X2 + 2
[active](X) = X
[isList](X) = 2.X + 2
[isNeList](X) = 2.X + 2
[isNePal](X) = 2.X + 2
[isPal](X) = 2.X + 2
[isQid](X) = X + 1
[mark](X) = X
[a] = 2
[e] = 2
[fSNonEmpty] = 0
[i] = 2
[nil] = 2
[o] = 2
[tt] = 2
[u] = 2
[U11#](X) = 0
[U21#](X1,X2) = 0
[U22#](X) = 0
[U31#](X) = 0
[U41#](X1,X2) = 0
[U42#](X) = 0
[U51#](X1,X2) = 0
[U52#](X) = 0
[U61#](X) = 0
[U71#](X1,X2) = 0
[U72#](X) = 0
[U81#](X) = 0
[__#](X1,X2) = 0
[ACTIVE](X) = 2.X + 2
[ISLIST](X) = 0
[ISNELIST](X) = 0
[ISNEPAL](X) = 0
[ISPAL](X) = 0
[ISQID](X) = 0
[MARK](X) = 2.X + 2

Problem 1.19: 

SCC Processor:
-> Pairs:
 ACTIVE(__(__(X:S,Y:S),Z:S)) -> MARK(__(X:S,__(Y:S,Z:S)))
 ACTIVE(__(nil,X:S)) -> MARK(X:S)
 ACTIVE(__(X:S,nil)) -> MARK(X:S)
 ACTIVE(isList(__(V1:S,V2:S))) -> MARK(U21(isList(V1:S),V2:S))
 ACTIVE(isList(V:S)) -> MARK(U11(isNeList(V:S)))
 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U41(isList(V1:S),V2:S))
 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U51(isNeList(V1:S),V2:S))
 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S)))
 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S))
 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S)))
 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S)))
 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S)))
 MARK(U11(X:S)) -> MARK(X:S)
 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S))
 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S)))
 MARK(U22(X:S)) -> MARK(X:S)
 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S)))
 MARK(U31(X:S)) -> MARK(X:S)
 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S))
 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S)))
 MARK(U42(X:S)) -> MARK(X:S)
 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S))
 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S)))
 MARK(U52(X:S)) -> MARK(X:S)
 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S)))
 MARK(U61(X:S)) -> MARK(X:S)
 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S))
 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S)))
 MARK(U72(X:S)) -> MARK(X:S)
 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S)))
 MARK(U81(X:S)) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(isList(X:S)) -> ACTIVE(isList(X:S))
 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S))
 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ACTIVE(__(__(X:S,Y:S),Z:S)) -> MARK(__(X:S,__(Y:S,Z:S)))
 ACTIVE(__(nil,X:S)) -> MARK(X:S)
 ACTIVE(__(X:S,nil)) -> MARK(X:S)
 ACTIVE(isList(__(V1:S,V2:S))) -> MARK(U21(isList(V1:S),V2:S))
 ACTIVE(isList(V:S)) -> MARK(U11(isNeList(V:S)))
 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U41(isList(V1:S),V2:S))
 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U51(isNeList(V1:S),V2:S))
 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S)))
 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S))
 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S)))
 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S)))
 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S)))
 MARK(U11(X:S)) -> MARK(X:S)
 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S))
 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S)))
 MARK(U22(X:S)) -> MARK(X:S)
 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S)))
 MARK(U31(X:S)) -> MARK(X:S)
 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S))
 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S)))
 MARK(U42(X:S)) -> MARK(X:S)
 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S))
 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S)))
 MARK(U52(X:S)) -> MARK(X:S)
 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S)))
 MARK(U61(X:S)) -> MARK(X:S)
 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S))
 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S)))
 MARK(U72(X:S)) -> MARK(X:S)
 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S)))
 MARK(U81(X:S)) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(isList(X:S)) -> ACTIVE(isList(X:S))
 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S))
 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
->->-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)

Problem 1.19: 

Reduction Pairs Processor:
-> Pairs:
 ACTIVE(__(__(X:S,Y:S),Z:S)) -> MARK(__(X:S,__(Y:S,Z:S)))
 ACTIVE(__(nil,X:S)) -> MARK(X:S)
 ACTIVE(__(X:S,nil)) -> MARK(X:S)
 ACTIVE(isList(__(V1:S,V2:S))) -> MARK(U21(isList(V1:S),V2:S))
 ACTIVE(isList(V:S)) -> MARK(U11(isNeList(V:S)))
 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U41(isList(V1:S),V2:S))
 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U51(isNeList(V1:S),V2:S))
 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S)))
 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S))
 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S)))
 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S)))
 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S)))
 MARK(U11(X:S)) -> MARK(X:S)
 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S))
 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S)))
 MARK(U22(X:S)) -> MARK(X:S)
 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S)))
 MARK(U31(X:S)) -> MARK(X:S)
 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S))
 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S)))
 MARK(U42(X:S)) -> MARK(X:S)
 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S))
 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S)))
 MARK(U52(X:S)) -> MARK(X:S)
 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S)))
 MARK(U61(X:S)) -> MARK(X:S)
 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S))
 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S)))
 MARK(U72(X:S)) -> MARK(X:S)
 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S)))
 MARK(U81(X:S)) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(isList(X:S)) -> ACTIVE(isList(X:S))
 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S))
 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
-> Usable rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[U11](X) = X
[U21](X1,X2) = 2.X1 + X2
[U22](X) = X + 2
[U31](X) = X
[U41](X1,X2) = X1 + X2 + 2
[U42](X) = X + 2
[U51](X1,X2) = 2.X1 + X2
[U52](X) = X + 2
[U61](X) = X
[U71](X1,X2) = 2.X1 + 2.X2
[U72](X) = X + 1
[U81](X) = X
[__](X1,X2) = 2.X1 + X2 + 2
[active](X) = X
[isList](X) = X + 2
[isNeList](X) = X + 2
[isNePal](X) = 2.X + 2
[isPal](X) = 2.X + 2
[isQid](X) = X + 2
[mark](X) = X
[a] = 0
[e] = 2
[fSNonEmpty] = 0
[i] = 2
[nil] = 2
[o] = 2
[tt] = 2
[u] = 2
[U11#](X) = 0
[U21#](X1,X2) = 0
[U22#](X) = 0
[U31#](X) = 0
[U41#](X1,X2) = 0
[U42#](X) = 0
[U51#](X1,X2) = 0
[U52#](X) = 0
[U61#](X) = 0
[U71#](X1,X2) = 0
[U72#](X) = 0
[U81#](X) = 0
[__#](X1,X2) = 0
[ACTIVE](X) = 2.X + 2
[ISLIST](X) = 0
[ISNELIST](X) = 0
[ISNEPAL](X) = 0
[ISPAL](X) = 0
[ISQID](X) = 0
[MARK](X) = 2.X + 2

Problem 1.19: 

SCC Processor:
-> Pairs:
 ACTIVE(__(nil,X:S)) -> MARK(X:S)
 ACTIVE(__(X:S,nil)) -> MARK(X:S)
 ACTIVE(isList(__(V1:S,V2:S))) -> MARK(U21(isList(V1:S),V2:S))
 ACTIVE(isList(V:S)) -> MARK(U11(isNeList(V:S)))
 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U41(isList(V1:S),V2:S))
 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U51(isNeList(V1:S),V2:S))
 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S)))
 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S))
 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S)))
 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S)))
 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S)))
 MARK(U11(X:S)) -> MARK(X:S)
 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S))
 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S)))
 MARK(U22(X:S)) -> MARK(X:S)
 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S)))
 MARK(U31(X:S)) -> MARK(X:S)
 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S))
 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S)))
 MARK(U42(X:S)) -> MARK(X:S)
 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S))
 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S)))
 MARK(U52(X:S)) -> MARK(X:S)
 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S)))
 MARK(U61(X:S)) -> MARK(X:S)
 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S))
 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S)))
 MARK(U72(X:S)) -> MARK(X:S)
 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S)))
 MARK(U81(X:S)) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(isList(X:S)) -> ACTIVE(isList(X:S))
 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S))
 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ACTIVE(__(nil,X:S)) -> MARK(X:S)
 ACTIVE(__(X:S,nil)) -> MARK(X:S)
 ACTIVE(isList(__(V1:S,V2:S))) -> MARK(U21(isList(V1:S),V2:S))
 ACTIVE(isList(V:S)) -> MARK(U11(isNeList(V:S)))
 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U41(isList(V1:S),V2:S))
 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U51(isNeList(V1:S),V2:S))
 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S)))
 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S))
 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S)))
 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S)))
 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S)))
 MARK(U11(X:S)) -> MARK(X:S)
 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S))
 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S)))
 MARK(U22(X:S)) -> MARK(X:S)
 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S)))
 MARK(U31(X:S)) -> MARK(X:S)
 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S))
 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S)))
 MARK(U42(X:S)) -> MARK(X:S)
 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S))
 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S)))
 MARK(U52(X:S)) -> MARK(X:S)
 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S)))
 MARK(U61(X:S)) -> MARK(X:S)
 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S))
 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S)))
 MARK(U72(X:S)) -> MARK(X:S)
 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S)))
 MARK(U81(X:S)) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(isList(X:S)) -> ACTIVE(isList(X:S))
 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S))
 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
->->-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)

Problem 1.19: 

Reduction Pairs Processor:
-> Pairs:
 ACTIVE(__(nil,X:S)) -> MARK(X:S)
 ACTIVE(__(X:S,nil)) -> MARK(X:S)
 ACTIVE(isList(__(V1:S,V2:S))) -> MARK(U21(isList(V1:S),V2:S))
 ACTIVE(isList(V:S)) -> MARK(U11(isNeList(V:S)))
 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U41(isList(V1:S),V2:S))
 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U51(isNeList(V1:S),V2:S))
 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S)))
 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S))
 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S)))
 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S)))
 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S)))
 MARK(U11(X:S)) -> MARK(X:S)
 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S))
 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S)))
 MARK(U22(X:S)) -> MARK(X:S)
 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S)))
 MARK(U31(X:S)) -> MARK(X:S)
 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S))
 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S)))
 MARK(U42(X:S)) -> MARK(X:S)
 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S))
 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S)))
 MARK(U52(X:S)) -> MARK(X:S)
 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S)))
 MARK(U61(X:S)) -> MARK(X:S)
 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S))
 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S)))
 MARK(U72(X:S)) -> MARK(X:S)
 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S)))
 MARK(U81(X:S)) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(isList(X:S)) -> ACTIVE(isList(X:S))
 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S))
 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
-> Usable rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[U11](X) = X
[U21](X1,X2) = X1 + 2.X2 + 2
[U22](X) = X + 2
[U31](X) = X + 1
[U41](X1,X2) = 2.X1 + 2.X2 + 1
[U42](X) = X + 2
[U51](X1,X2) = X1 + 2.X2 + 2
[U52](X) = X
[U61](X) = X + 2
[U71](X1,X2) = 2.X1 + 2.X2 + 2
[U72](X) = X + 1
[U81](X) = X
[__](X1,X2) = 2.X1 + X2 + 2
[active](X) = X
[isList](X) = 2.X + 2
[isNeList](X) = 2.X + 2
[isNePal](X) = 2.X + 2
[isPal](X) = 2.X + 2
[isQid](X) = 2.X
[mark](X) = X
[a] = 2
[e] = 1
[fSNonEmpty] = 0
[i] = 2
[nil] = 2
[o] = 2
[tt] = 2
[u] = 2
[U11#](X) = 0
[U21#](X1,X2) = 0
[U22#](X) = 0
[U31#](X) = 0
[U41#](X1,X2) = 0
[U42#](X) = 0
[U51#](X1,X2) = 0
[U52#](X) = 0
[U61#](X) = 0
[U71#](X1,X2) = 0
[U72#](X) = 0
[U81#](X) = 0
[__#](X1,X2) = 0
[ACTIVE](X) = 2.X + 2
[ISLIST](X) = 0
[ISNELIST](X) = 0
[ISNEPAL](X) = 0
[ISPAL](X) = 0
[ISQID](X) = 0
[MARK](X) = 2.X + 2

Problem 1.19: 

SCC Processor:
-> Pairs:
 ACTIVE(__(X:S,nil)) -> MARK(X:S)
 ACTIVE(isList(__(V1:S,V2:S))) -> MARK(U21(isList(V1:S),V2:S))
 ACTIVE(isList(V:S)) -> MARK(U11(isNeList(V:S)))
 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U41(isList(V1:S),V2:S))
 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U51(isNeList(V1:S),V2:S))
 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S)))
 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S))
 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S)))
 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S)))
 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S)))
 MARK(U11(X:S)) -> MARK(X:S)
 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S))
 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S)))
 MARK(U22(X:S)) -> MARK(X:S)
 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S)))
 MARK(U31(X:S)) -> MARK(X:S)
 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S))
 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S)))
 MARK(U42(X:S)) -> MARK(X:S)
 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S))
 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S)))
 MARK(U52(X:S)) -> MARK(X:S)
 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S)))
 MARK(U61(X:S)) -> MARK(X:S)
 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S))
 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S)))
 MARK(U72(X:S)) -> MARK(X:S)
 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S)))
 MARK(U81(X:S)) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(isList(X:S)) -> ACTIVE(isList(X:S))
 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S))
 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ACTIVE(__(X:S,nil)) -> MARK(X:S)
 ACTIVE(isList(__(V1:S,V2:S))) -> MARK(U21(isList(V1:S),V2:S))
 ACTIVE(isList(V:S)) -> MARK(U11(isNeList(V:S)))
 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U41(isList(V1:S),V2:S))
 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U51(isNeList(V1:S),V2:S))
 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S)))
 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S))
 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S)))
 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S)))
 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S)))
 MARK(U11(X:S)) -> MARK(X:S)
 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S))
 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S)))
 MARK(U22(X:S)) -> MARK(X:S)
 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S)))
 MARK(U31(X:S)) -> MARK(X:S)
 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S))
 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S)))
 MARK(U42(X:S)) -> MARK(X:S)
 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S))
 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S)))
 MARK(U52(X:S)) -> MARK(X:S)
 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S)))
 MARK(U61(X:S)) -> MARK(X:S)
 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S))
 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S)))
 MARK(U72(X:S)) -> MARK(X:S)
 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S)))
 MARK(U81(X:S)) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(isList(X:S)) -> ACTIVE(isList(X:S))
 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S))
 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
->->-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)

Problem 1.19: 

Reduction Pairs Processor:
-> Pairs:
 ACTIVE(__(X:S,nil)) -> MARK(X:S)
 ACTIVE(isList(__(V1:S,V2:S))) -> MARK(U21(isList(V1:S),V2:S))
 ACTIVE(isList(V:S)) -> MARK(U11(isNeList(V:S)))
 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U41(isList(V1:S),V2:S))
 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U51(isNeList(V1:S),V2:S))
 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S)))
 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S))
 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S)))
 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S)))
 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S)))
 MARK(U11(X:S)) -> MARK(X:S)
 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S))
 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S)))
 MARK(U22(X:S)) -> MARK(X:S)
 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S)))
 MARK(U31(X:S)) -> MARK(X:S)
 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S))
 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S)))
 MARK(U42(X:S)) -> MARK(X:S)
 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S))
 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S)))
 MARK(U52(X:S)) -> MARK(X:S)
 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S)))
 MARK(U61(X:S)) -> MARK(X:S)
 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S))
 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S)))
 MARK(U72(X:S)) -> MARK(X:S)
 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S)))
 MARK(U81(X:S)) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(isList(X:S)) -> ACTIVE(isList(X:S))
 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S))
 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
-> Usable rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[U11](X) = X
[U21](X1,X2) = X1
[U22](X) = X
[U31](X) = X
[U41](X1,X2) = X1
[U42](X) = X
[U51](X1,X2) = X1
[U52](X) = X
[U61](X) = X
[U71](X1,X2) = 2.X1 + 2.X2 + 2
[U72](X) = 2.X
[U81](X) = X
[__](X1,X2) = 2.X1 + X2 + 2
[active](X) = X
[isList](X) = 2
[isNeList](X) = 2
[isNePal](X) = X + 2
[isPal](X) = X + 2
[isQid](X) = 2
[mark](X) = X
[a] = 2
[e] = 2
[fSNonEmpty] = 0
[i] = 1
[nil] = 2
[o] = 0
[tt] = 2
[u] = 2
[U11#](X) = 0
[U21#](X1,X2) = 0
[U22#](X) = 0
[U31#](X) = 0
[U41#](X1,X2) = 0
[U42#](X) = 0
[U51#](X1,X2) = 0
[U52#](X) = 0
[U61#](X) = 0
[U71#](X1,X2) = 0
[U72#](X) = 0
[U81#](X) = 0
[__#](X1,X2) = 0
[ACTIVE](X) = 2.X + 1
[ISLIST](X) = 0
[ISNELIST](X) = 0
[ISNEPAL](X) = 0
[ISPAL](X) = 0
[ISQID](X) = 0
[MARK](X) = 2.X + 1

Problem 1.19: 

SCC Processor:
-> Pairs:
 ACTIVE(isList(__(V1:S,V2:S))) -> MARK(U21(isList(V1:S),V2:S))
 ACTIVE(isList(V:S)) -> MARK(U11(isNeList(V:S)))
 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U41(isList(V1:S),V2:S))
 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U51(isNeList(V1:S),V2:S))
 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S)))
 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S))
 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S)))
 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S)))
 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S)))
 MARK(U11(X:S)) -> MARK(X:S)
 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S))
 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S)))
 MARK(U22(X:S)) -> MARK(X:S)
 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S)))
 MARK(U31(X:S)) -> MARK(X:S)
 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S))
 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S)))
 MARK(U42(X:S)) -> MARK(X:S)
 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S))
 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S)))
 MARK(U52(X:S)) -> MARK(X:S)
 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S)))
 MARK(U61(X:S)) -> MARK(X:S)
 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S))
 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S)))
 MARK(U72(X:S)) -> MARK(X:S)
 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S)))
 MARK(U81(X:S)) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(isList(X:S)) -> ACTIVE(isList(X:S))
 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S))
 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ACTIVE(isList(__(V1:S,V2:S))) -> MARK(U21(isList(V1:S),V2:S))
 ACTIVE(isList(V:S)) -> MARK(U11(isNeList(V:S)))
 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U41(isList(V1:S),V2:S))
 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U51(isNeList(V1:S),V2:S))
 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S)))
 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S))
 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S)))
 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S)))
 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S)))
 MARK(U11(X:S)) -> MARK(X:S)
 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S))
 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S)))
 MARK(U22(X:S)) -> MARK(X:S)
 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S)))
 MARK(U31(X:S)) -> MARK(X:S)
 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S))
 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S)))
 MARK(U42(X:S)) -> MARK(X:S)
 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S))
 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S)))
 MARK(U52(X:S)) -> MARK(X:S)
 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S)))
 MARK(U61(X:S)) -> MARK(X:S)
 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S))
 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S)))
 MARK(U72(X:S)) -> MARK(X:S)
 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S)))
 MARK(U81(X:S)) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(isList(X:S)) -> ACTIVE(isList(X:S))
 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S))
 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
->->-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)

Problem 1.19: 

Reduction Pairs Processor:
-> Pairs:
 ACTIVE(isList(__(V1:S,V2:S))) -> MARK(U21(isList(V1:S),V2:S))
 ACTIVE(isList(V:S)) -> MARK(U11(isNeList(V:S)))
 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U41(isList(V1:S),V2:S))
 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U51(isNeList(V1:S),V2:S))
 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S)))
 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S))
 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S)))
 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S)))
 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S)))
 MARK(U11(X:S)) -> MARK(X:S)
 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S))
 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S)))
 MARK(U22(X:S)) -> MARK(X:S)
 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S)))
 MARK(U31(X:S)) -> MARK(X:S)
 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S))
 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S)))
 MARK(U42(X:S)) -> MARK(X:S)
 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S))
 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S)))
 MARK(U52(X:S)) -> MARK(X:S)
 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S)))
 MARK(U61(X:S)) -> MARK(X:S)
 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S))
 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S)))
 MARK(U72(X:S)) -> MARK(X:S)
 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S)))
 MARK(U81(X:S)) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(isList(X:S)) -> ACTIVE(isList(X:S))
 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S))
 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
-> Usable rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[U11](X) = X + 2
[U21](X1,X2) = X1 + 2.X2 + 2
[U22](X) = X + 2
[U31](X) = 2.X
[U41](X1,X2) = X1 + 2.X2 + 2
[U42](X) = X + 2
[U51](X1,X2) = 2.X1 + 2.X2
[U52](X) = X + 2
[U61](X) = 2.X
[U71](X1,X2) = 2.X1 + 2.X2 + 2
[U72](X) = X + 2
[U81](X) = X + 2
[__](X1,X2) = 2.X1 + X2 + 2
[active](X) = X
[isList](X) = 2.X + 2
[isNeList](X) = 2.X
[isNePal](X) = 2.X
[isPal](X) = 2.X + 2
[isQid](X) = X
[mark](X) = X
[a] = 2
[e] = 2
[fSNonEmpty] = 0
[i] = 2
[nil] = 1
[o] = 2
[tt] = 2
[u] = 2
[U11#](X) = 0
[U21#](X1,X2) = 0
[U22#](X) = 0
[U31#](X) = 0
[U41#](X1,X2) = 0
[U42#](X) = 0
[U51#](X1,X2) = 0
[U52#](X) = 0
[U61#](X) = 0
[U71#](X1,X2) = 0
[U72#](X) = 0
[U81#](X) = 0
[__#](X1,X2) = 0
[ACTIVE](X) = X + 2
[ISLIST](X) = 0
[ISNELIST](X) = 0
[ISNEPAL](X) = 0
[ISPAL](X) = 0
[ISQID](X) = 0
[MARK](X) = X + 2

Problem 1.19: 

SCC Processor:
-> Pairs:
 ACTIVE(isList(V:S)) -> MARK(U11(isNeList(V:S)))
 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U41(isList(V1:S),V2:S))
 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U51(isNeList(V1:S),V2:S))
 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S)))
 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S))
 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S)))
 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S)))
 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S)))
 MARK(U11(X:S)) -> MARK(X:S)
 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S))
 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S)))
 MARK(U22(X:S)) -> MARK(X:S)
 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S)))
 MARK(U31(X:S)) -> MARK(X:S)
 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S))
 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S)))
 MARK(U42(X:S)) -> MARK(X:S)
 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S))
 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S)))
 MARK(U52(X:S)) -> MARK(X:S)
 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S)))
 MARK(U61(X:S)) -> MARK(X:S)
 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S))
 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S)))
 MARK(U72(X:S)) -> MARK(X:S)
 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S)))
 MARK(U81(X:S)) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(isList(X:S)) -> ACTIVE(isList(X:S))
 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S))
 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ACTIVE(isList(V:S)) -> MARK(U11(isNeList(V:S)))
 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U41(isList(V1:S),V2:S))
 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U51(isNeList(V1:S),V2:S))
 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S)))
 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S))
 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S)))
 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S)))
 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S)))
 MARK(U11(X:S)) -> MARK(X:S)
 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S))
 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S)))
 MARK(U22(X:S)) -> MARK(X:S)
 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S)))
 MARK(U31(X:S)) -> MARK(X:S)
 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S))
 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S)))
 MARK(U42(X:S)) -> MARK(X:S)
 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S))
 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S)))
 MARK(U52(X:S)) -> MARK(X:S)
 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S)))
 MARK(U61(X:S)) -> MARK(X:S)
 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S))
 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S)))
 MARK(U72(X:S)) -> MARK(X:S)
 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S)))
 MARK(U81(X:S)) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(isList(X:S)) -> ACTIVE(isList(X:S))
 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S))
 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
->->-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)

Problem 1.19: 

Reduction Pairs Processor:
-> Pairs:
 ACTIVE(isList(V:S)) -> MARK(U11(isNeList(V:S)))
 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U41(isList(V1:S),V2:S))
 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U51(isNeList(V1:S),V2:S))
 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S)))
 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S))
 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S)))
 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S)))
 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S)))
 MARK(U11(X:S)) -> MARK(X:S)
 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S))
 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S)))
 MARK(U22(X:S)) -> MARK(X:S)
 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S)))
 MARK(U31(X:S)) -> MARK(X:S)
 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S))
 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S)))
 MARK(U42(X:S)) -> MARK(X:S)
 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S))
 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S)))
 MARK(U52(X:S)) -> MARK(X:S)
 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S)))
 MARK(U61(X:S)) -> MARK(X:S)
 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S))
 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S)))
 MARK(U72(X:S)) -> MARK(X:S)
 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S)))
 MARK(U81(X:S)) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(isList(X:S)) -> ACTIVE(isList(X:S))
 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S))
 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
-> Usable rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[U11](X) = X
[U21](X1,X2) = 2.X1 + 2.X2 + 2
[U22](X) = X + 2
[U31](X) = X
[U41](X1,X2) = X1 + 2.X2 + 2
[U42](X) = X + 2
[U51](X1,X2) = 2.X1 + 2.X2 + 2
[U52](X) = X
[U61](X) = X + 1
[U71](X1,X2) = 2.X1 + 2.X2 + 2
[U72](X) = 2.X
[U81](X) = X
[__](X1,X2) = 2.X1 + X2 + 2
[active](X) = X
[isList](X) = 2.X + 2
[isNeList](X) = 2.X + 1
[isNePal](X) = X + 2
[isPal](X) = X + 2
[isQid](X) = X + 1
[mark](X) = X
[a] = 2
[e] = 1
[fSNonEmpty] = 0
[i] = 2
[nil] = 2
[o] = 1
[tt] = 2
[u] = 1
[U11#](X) = 0
[U21#](X1,X2) = 0
[U22#](X) = 0
[U31#](X) = 0
[U41#](X1,X2) = 0
[U42#](X) = 0
[U51#](X1,X2) = 0
[U52#](X) = 0
[U61#](X) = 0
[U71#](X1,X2) = 0
[U72#](X) = 0
[U81#](X) = 0
[__#](X1,X2) = 0
[ACTIVE](X) = 2.X + 2
[ISLIST](X) = 0
[ISNELIST](X) = 0
[ISNEPAL](X) = 0
[ISPAL](X) = 0
[ISQID](X) = 0
[MARK](X) = 2.X + 2

Problem 1.19: 

SCC Processor:
-> Pairs:
 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U41(isList(V1:S),V2:S))
 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U51(isNeList(V1:S),V2:S))
 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S)))
 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S))
 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S)))
 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S)))
 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S)))
 MARK(U11(X:S)) -> MARK(X:S)
 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S))
 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S)))
 MARK(U22(X:S)) -> MARK(X:S)
 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S)))
 MARK(U31(X:S)) -> MARK(X:S)
 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S))
 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S)))
 MARK(U42(X:S)) -> MARK(X:S)
 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S))
 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S)))
 MARK(U52(X:S)) -> MARK(X:S)
 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S)))
 MARK(U61(X:S)) -> MARK(X:S)
 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S))
 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S)))
 MARK(U72(X:S)) -> MARK(X:S)
 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S)))
 MARK(U81(X:S)) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(isList(X:S)) -> ACTIVE(isList(X:S))
 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S))
 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U41(isList(V1:S),V2:S))
 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U51(isNeList(V1:S),V2:S))
 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S)))
 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S))
 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S)))
 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S)))
 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S)))
 MARK(U11(X:S)) -> MARK(X:S)
 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S))
 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S)))
 MARK(U22(X:S)) -> MARK(X:S)
 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S)))
 MARK(U31(X:S)) -> MARK(X:S)
 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S))
 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S)))
 MARK(U42(X:S)) -> MARK(X:S)
 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S))
 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S)))
 MARK(U52(X:S)) -> MARK(X:S)
 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S)))
 MARK(U61(X:S)) -> MARK(X:S)
 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S))
 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S)))
 MARK(U72(X:S)) -> MARK(X:S)
 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S)))
 MARK(U81(X:S)) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S))
 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
->->-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)

Problem 1.19: 

Reduction Pairs Processor:
-> Pairs:
 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U41(isList(V1:S),V2:S))
 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U51(isNeList(V1:S),V2:S))
 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S)))
 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S))
 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S)))
 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S)))
 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S)))
 MARK(U11(X:S)) -> MARK(X:S)
 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S))
 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S)))
 MARK(U22(X:S)) -> MARK(X:S)
 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S)))
 MARK(U31(X:S)) -> MARK(X:S)
 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S))
 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S)))
 MARK(U42(X:S)) -> MARK(X:S)
 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S))
 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S)))
 MARK(U52(X:S)) -> MARK(X:S)
 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S)))
 MARK(U61(X:S)) -> MARK(X:S)
 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S))
 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S)))
 MARK(U72(X:S)) -> MARK(X:S)
 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S)))
 MARK(U81(X:S)) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S))
 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
-> Usable rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[U11](X) = X
[U21](X1,X2) = 2.X1 + 2.X2 + 2
[U22](X) = X
[U31](X) = X + 1
[U41](X1,X2) = 2.X1 + 2.X2 + 1
[U42](X) = X + 2
[U51](X1,X2) = 2.X1 + 2.X2 + 2
[U52](X) = X + 1
[U61](X) = X
[U71](X1,X2) = 2.X1 + 2.X2 + 2
[U72](X) = X
[U81](X) = 2.X
[__](X1,X2) = 2.X1 + X2 + 2
[active](X) = X
[isList](X) = 2.X + 2
[isNeList](X) = 2.X + 2
[isNePal](X) = X + 1
[isPal](X) = 2.X + 2
[isQid](X) = X + 1
[mark](X) = X
[a] = 2
[e] = 2
[fSNonEmpty] = 0
[i] = 2
[nil] = 2
[o] = 2
[tt] = 2
[u] = 2
[U11#](X) = 0
[U21#](X1,X2) = 0
[U22#](X) = 0
[U31#](X) = 0
[U41#](X1,X2) = 0
[U42#](X) = 0
[U51#](X1,X2) = 0
[U52#](X) = 0
[U61#](X) = 0
[U71#](X1,X2) = 0
[U72#](X) = 0
[U81#](X) = 0
[__#](X1,X2) = 0
[ACTIVE](X) = 2.X
[ISLIST](X) = 0
[ISNELIST](X) = 0
[ISNEPAL](X) = 0
[ISPAL](X) = 0
[ISQID](X) = 0
[MARK](X) = 2.X

Problem 1.19: 

SCC Processor:
-> Pairs:
 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U51(isNeList(V1:S),V2:S))
 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S)))
 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S))
 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S)))
 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S)))
 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S)))
 MARK(U11(X:S)) -> MARK(X:S)
 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S))
 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S)))
 MARK(U22(X:S)) -> MARK(X:S)
 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S)))
 MARK(U31(X:S)) -> MARK(X:S)
 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S))
 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S)))
 MARK(U42(X:S)) -> MARK(X:S)
 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S))
 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S)))
 MARK(U52(X:S)) -> MARK(X:S)
 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S)))
 MARK(U61(X:S)) -> MARK(X:S)
 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S))
 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S)))
 MARK(U72(X:S)) -> MARK(X:S)
 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S)))
 MARK(U81(X:S)) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S))
 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U51(isNeList(V1:S),V2:S))
 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S)))
 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S))
 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S)))
 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S)))
 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S)))
 MARK(U11(X:S)) -> MARK(X:S)
 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S))
 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S)))
 MARK(U22(X:S)) -> MARK(X:S)
 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S)))
 MARK(U31(X:S)) -> MARK(X:S)
 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S))
 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S)))
 MARK(U42(X:S)) -> MARK(X:S)
 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S))
 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S)))
 MARK(U52(X:S)) -> MARK(X:S)
 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S)))
 MARK(U61(X:S)) -> MARK(X:S)
 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S))
 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S)))
 MARK(U72(X:S)) -> MARK(X:S)
 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S)))
 MARK(U81(X:S)) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S))
 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
->->-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)

Problem 1.19: 

Reduction Pairs Processor:
-> Pairs:
 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U51(isNeList(V1:S),V2:S))
 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S)))
 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S))
 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S)))
 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S)))
 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S)))
 MARK(U11(X:S)) -> MARK(X:S)
 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S))
 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S)))
 MARK(U22(X:S)) -> MARK(X:S)
 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S)))
 MARK(U31(X:S)) -> MARK(X:S)
 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S))
 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S)))
 MARK(U42(X:S)) -> MARK(X:S)
 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S))
 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S)))
 MARK(U52(X:S)) -> MARK(X:S)
 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S)))
 MARK(U61(X:S)) -> MARK(X:S)
 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S))
 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S)))
 MARK(U72(X:S)) -> MARK(X:S)
 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S)))
 MARK(U81(X:S)) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S))
 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
-> Usable rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[U11](X) = X
[U21](X1,X2) = X1 + 2.X2 + 2
[U22](X) = X + 1
[U31](X) = X + 1
[U41](X1,X2) = X1 + 2.X2 + 2
[U42](X) = X + 1
[U51](X1,X2) = 2.X1 + 2.X2 + 1
[U52](X) = X + 1
[U61](X) = X
[U71](X1,X2) = 2.X1 + 2.X2
[U72](X) = X + 2
[U81](X) = X + 1
[__](X1,X2) = 2.X1 + X2 + 2
[active](X) = X
[isList](X) = 2.X + 2
[isNeList](X) = 2.X + 2
[isNePal](X) = 2.X + 1
[isPal](X) = 2.X + 2
[isQid](X) = 2.X + 1
[mark](X) = X
[a] = 1
[e] = 2
[fSNonEmpty] = 0
[i] = 2
[nil] = 2
[o] = 2
[tt] = 2
[u] = 2
[U11#](X) = 0
[U21#](X1,X2) = 0
[U22#](X) = 0
[U31#](X) = 0
[U41#](X1,X2) = 0
[U42#](X) = 0
[U51#](X1,X2) = 0
[U52#](X) = 0
[U61#](X) = 0
[U71#](X1,X2) = 0
[U72#](X) = 0
[U81#](X) = 0
[__#](X1,X2) = 0
[ACTIVE](X) = 2.X + 2
[ISLIST](X) = 0
[ISNELIST](X) = 0
[ISNEPAL](X) = 0
[ISPAL](X) = 0
[ISQID](X) = 0
[MARK](X) = 2.X + 2

Problem 1.19: 

SCC Processor:
-> Pairs:
 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S)))
 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S))
 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S)))
 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S)))
 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S)))
 MARK(U11(X:S)) -> MARK(X:S)
 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S))
 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S)))
 MARK(U22(X:S)) -> MARK(X:S)
 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S)))
 MARK(U31(X:S)) -> MARK(X:S)
 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S))
 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S)))
 MARK(U42(X:S)) -> MARK(X:S)
 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S))
 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S)))
 MARK(U52(X:S)) -> MARK(X:S)
 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S)))
 MARK(U61(X:S)) -> MARK(X:S)
 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S))
 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S)))
 MARK(U72(X:S)) -> MARK(X:S)
 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S)))
 MARK(U81(X:S)) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S))
 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S)))
 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S))
 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S)))
 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S)))
 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S)))
 MARK(U11(X:S)) -> MARK(X:S)
 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S))
 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S)))
 MARK(U22(X:S)) -> MARK(X:S)
 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S)))
 MARK(U31(X:S)) -> MARK(X:S)
 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S))
 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S)))
 MARK(U42(X:S)) -> MARK(X:S)
 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S))
 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S)))
 MARK(U52(X:S)) -> MARK(X:S)
 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S)))
 MARK(U61(X:S)) -> MARK(X:S)
 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S))
 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S)))
 MARK(U72(X:S)) -> MARK(X:S)
 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S)))
 MARK(U81(X:S)) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S))
 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
->->-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)

Problem 1.19: 

Reduction Pairs Processor:
-> Pairs:
 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S)))
 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S))
 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S)))
 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S)))
 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S)))
 MARK(U11(X:S)) -> MARK(X:S)
 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S))
 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S)))
 MARK(U22(X:S)) -> MARK(X:S)
 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S)))
 MARK(U31(X:S)) -> MARK(X:S)
 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S))
 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S)))
 MARK(U42(X:S)) -> MARK(X:S)
 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S))
 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S)))
 MARK(U52(X:S)) -> MARK(X:S)
 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S)))
 MARK(U61(X:S)) -> MARK(X:S)
 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S))
 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S)))
 MARK(U72(X:S)) -> MARK(X:S)
 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S)))
 MARK(U81(X:S)) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S))
 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
-> Usable rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[U11](X) = X
[U21](X1,X2) = 2.X1 + 2.X2 + 1
[U22](X) = X + 2
[U31](X) = X
[U41](X1,X2) = X1 + 2.X2 + 2
[U42](X) = X + 2
[U51](X1,X2) = 2.X1 + 2.X2 + 2
[U52](X) = X + 2
[U61](X) = X + 1
[U71](X1,X2) = 2.X1 + 2.X2
[U72](X) = X + 2
[U81](X) = X
[__](X1,X2) = 2.X1 + X2 + 2
[active](X) = X
[isList](X) = 2.X + 2
[isNeList](X) = 2.X + 2
[isNePal](X) = X + 2
[isPal](X) = 2.X + 2
[isQid](X) = X + 1
[mark](X) = X
[a] = 2
[e] = 2
[fSNonEmpty] = 0
[i] = 2
[nil] = 2
[o] = 1
[tt] = 2
[u] = 2
[U11#](X) = 0
[U21#](X1,X2) = 0
[U22#](X) = 0
[U31#](X) = 0
[U41#](X1,X2) = 0
[U42#](X) = 0
[U51#](X1,X2) = 0
[U52#](X) = 0
[U61#](X) = 0
[U71#](X1,X2) = 0
[U72#](X) = 0
[U81#](X) = 0
[__#](X1,X2) = 0
[ACTIVE](X) = 2.X + 1
[ISLIST](X) = 0
[ISNELIST](X) = 0
[ISNEPAL](X) = 0
[ISPAL](X) = 0
[ISQID](X) = 0
[MARK](X) = 2.X + 1

Problem 1.19: 

SCC Processor:
-> Pairs:
 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S))
 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S)))
 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S)))
 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S)))
 MARK(U11(X:S)) -> MARK(X:S)
 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S))
 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S)))
 MARK(U22(X:S)) -> MARK(X:S)
 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S)))
 MARK(U31(X:S)) -> MARK(X:S)
 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S))
 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S)))
 MARK(U42(X:S)) -> MARK(X:S)
 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S))
 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S)))
 MARK(U52(X:S)) -> MARK(X:S)
 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S)))
 MARK(U61(X:S)) -> MARK(X:S)
 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S))
 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S)))
 MARK(U72(X:S)) -> MARK(X:S)
 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S)))
 MARK(U81(X:S)) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S))
 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S))
 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S)))
 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S)))
 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S)))
 MARK(U11(X:S)) -> MARK(X:S)
 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S))
 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S)))
 MARK(U22(X:S)) -> MARK(X:S)
 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S)))
 MARK(U31(X:S)) -> MARK(X:S)
 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S))
 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S)))
 MARK(U42(X:S)) -> MARK(X:S)
 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S))
 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S)))
 MARK(U52(X:S)) -> MARK(X:S)
 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S)))
 MARK(U61(X:S)) -> MARK(X:S)
 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S))
 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S)))
 MARK(U72(X:S)) -> MARK(X:S)
 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S)))
 MARK(U81(X:S)) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
->->-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)

Problem 1.19: 

Reduction Pairs Processor:
-> Pairs:
 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S))
 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S)))
 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S)))
 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S)))
 MARK(U11(X:S)) -> MARK(X:S)
 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S))
 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S)))
 MARK(U22(X:S)) -> MARK(X:S)
 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S)))
 MARK(U31(X:S)) -> MARK(X:S)
 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S))
 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S)))
 MARK(U42(X:S)) -> MARK(X:S)
 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S))
 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S)))
 MARK(U52(X:S)) -> MARK(X:S)
 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S)))
 MARK(U61(X:S)) -> MARK(X:S)
 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S))
 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S)))
 MARK(U72(X:S)) -> MARK(X:S)
 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S)))
 MARK(U81(X:S)) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
-> Usable rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[U11](X) = X
[U21](X1,X2) = 2.X1 + 2.X2 + 2
[U22](X) = X + 2
[U31](X) = X
[U41](X1,X2) = X1 + 2.X2 + 2
[U42](X) = X + 2
[U51](X1,X2) = 2.X1 + 2.X2
[U52](X) = X + 2
[U61](X) = X
[U71](X1,X2) = 2.X1 + 2.X2 + 2
[U72](X) = X + 2
[U81](X) = X
[__](X1,X2) = 2.X1 + X2 + 2
[active](X) = X
[isList](X) = 2.X + 2
[isNeList](X) = 2.X + 2
[isNePal](X) = 2.X + 2
[isPal](X) = 2.X + 2
[isQid](X) = 2.X + 2
[mark](X) = X
[a] = 2
[e] = 2
[fSNonEmpty] = 0
[i] = 2
[nil] = 2
[o] = 1
[tt] = 2
[u] = 1
[U11#](X) = 0
[U21#](X1,X2) = 0
[U22#](X) = 0
[U31#](X) = 0
[U41#](X1,X2) = 0
[U42#](X) = 0
[U51#](X1,X2) = 0
[U52#](X) = 0
[U61#](X) = 0
[U71#](X1,X2) = 0
[U72#](X) = 0
[U81#](X) = 0
[__#](X1,X2) = 0
[ACTIVE](X) = 2.X + 2
[ISLIST](X) = 0
[ISNELIST](X) = 0
[ISNEPAL](X) = 0
[ISPAL](X) = 0
[ISQID](X) = 0
[MARK](X) = 2.X + 2

Problem 1.19: 

SCC Processor:
-> Pairs:
 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S)))
 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S)))
 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S)))
 MARK(U11(X:S)) -> MARK(X:S)
 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S))
 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S)))
 MARK(U22(X:S)) -> MARK(X:S)
 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S)))
 MARK(U31(X:S)) -> MARK(X:S)
 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S))
 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S)))
 MARK(U42(X:S)) -> MARK(X:S)
 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S))
 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S)))
 MARK(U52(X:S)) -> MARK(X:S)
 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S)))
 MARK(U61(X:S)) -> MARK(X:S)
 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S))
 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S)))
 MARK(U72(X:S)) -> MARK(X:S)
 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S)))
 MARK(U81(X:S)) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S)))
 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S)))
 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S)))
 MARK(U11(X:S)) -> MARK(X:S)
 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S))
 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S)))
 MARK(U22(X:S)) -> MARK(X:S)
 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S)))
 MARK(U31(X:S)) -> MARK(X:S)
 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S))
 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S)))
 MARK(U42(X:S)) -> MARK(X:S)
 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S))
 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S)))
 MARK(U52(X:S)) -> MARK(X:S)
 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S)))
 MARK(U61(X:S)) -> MARK(X:S)
 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S))
 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S)))
 MARK(U72(X:S)) -> MARK(X:S)
 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S)))
 MARK(U81(X:S)) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
->->-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)

Problem 1.19: 

Reduction Pairs Processor:
-> Pairs:
 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S)))
 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S)))
 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S)))
 MARK(U11(X:S)) -> MARK(X:S)
 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S))
 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S)))
 MARK(U22(X:S)) -> MARK(X:S)
 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S)))
 MARK(U31(X:S)) -> MARK(X:S)
 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S))
 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S)))
 MARK(U42(X:S)) -> MARK(X:S)
 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S))
 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S)))
 MARK(U52(X:S)) -> MARK(X:S)
 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S)))
 MARK(U61(X:S)) -> MARK(X:S)
 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S))
 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S)))
 MARK(U72(X:S)) -> MARK(X:S)
 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S)))
 MARK(U81(X:S)) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
-> Usable rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[U11](X) = X
[U21](X1,X2) = 2.X1 + 2.X2 + 2
[U22](X) = X + 2
[U31](X) = 2.X + 2
[U41](X1,X2) = 2.X1 + 2.X2
[U42](X) = X
[U51](X1,X2) = 2.X1 + 2.X2 + 2
[U52](X) = X + 2
[U61](X) = X
[U71](X1,X2) = 2.X1 + 2.X2 + 2
[U72](X) = X + 2
[U81](X) = X
[__](X1,X2) = 2.X1 + X2 + 2
[active](X) = X
[isList](X) = 2.X + 2
[isNeList](X) = 2.X + 2
[isNePal](X) = 2.X + 2
[isPal](X) = 2.X + 2
[isQid](X) = X
[mark](X) = X
[a] = 2
[e] = 2
[fSNonEmpty] = 0
[i] = 2
[nil] = 1
[o] = 2
[tt] = 2
[u] = 2
[U11#](X) = 0
[U21#](X1,X2) = 0
[U22#](X) = 0
[U31#](X) = 0
[U41#](X1,X2) = 0
[U42#](X) = 0
[U51#](X1,X2) = 0
[U52#](X) = 0
[U61#](X) = 0
[U71#](X1,X2) = 0
[U72#](X) = 0
[U81#](X) = 0
[__#](X1,X2) = 0
[ACTIVE](X) = 2.X
[ISLIST](X) = 0
[ISNELIST](X) = 0
[ISNEPAL](X) = 0
[ISPAL](X) = 0
[ISQID](X) = 0
[MARK](X) = 2.X

Problem 1.19: 

SCC Processor:
-> Pairs:
 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S)))
 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S)))
 MARK(U11(X:S)) -> MARK(X:S)
 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S))
 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S)))
 MARK(U22(X:S)) -> MARK(X:S)
 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S)))
 MARK(U31(X:S)) -> MARK(X:S)
 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S))
 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S)))
 MARK(U42(X:S)) -> MARK(X:S)
 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S))
 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S)))
 MARK(U52(X:S)) -> MARK(X:S)
 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S)))
 MARK(U61(X:S)) -> MARK(X:S)
 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S))
 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S)))
 MARK(U72(X:S)) -> MARK(X:S)
 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S)))
 MARK(U81(X:S)) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S)))
 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S)))
 MARK(U11(X:S)) -> MARK(X:S)
 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S))
 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S)))
 MARK(U22(X:S)) -> MARK(X:S)
 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S)))
 MARK(U31(X:S)) -> MARK(X:S)
 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S))
 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S)))
 MARK(U42(X:S)) -> MARK(X:S)
 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S))
 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S)))
 MARK(U52(X:S)) -> MARK(X:S)
 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S)))
 MARK(U61(X:S)) -> MARK(X:S)
 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S))
 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S)))
 MARK(U72(X:S)) -> MARK(X:S)
 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S)))
 MARK(U81(X:S)) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
->->-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)

Problem 1.19: 

Reduction Pairs Processor:
-> Pairs:
 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S)))
 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S)))
 MARK(U11(X:S)) -> MARK(X:S)
 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S))
 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S)))
 MARK(U22(X:S)) -> MARK(X:S)
 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S)))
 MARK(U31(X:S)) -> MARK(X:S)
 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S))
 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S)))
 MARK(U42(X:S)) -> MARK(X:S)
 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S))
 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S)))
 MARK(U52(X:S)) -> MARK(X:S)
 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S)))
 MARK(U61(X:S)) -> MARK(X:S)
 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S))
 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S)))
 MARK(U72(X:S)) -> MARK(X:S)
 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S)))
 MARK(U81(X:S)) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
-> Usable rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[U11](X) = X
[U21](X1,X2) = X1 + 2.X2 + 2
[U22](X) = X + 2
[U31](X) = X + 2
[U41](X1,X2) = 2.X1 + 2.X2
[U42](X) = X + 2
[U51](X1,X2) = 2.X1 + 2.X2 + 1
[U52](X) = X + 2
[U61](X) = X
[U71](X1,X2) = 2.X1 + 2.X2 + 2
[U72](X) = X + 1
[U81](X) = X + 1
[__](X1,X2) = 2.X1 + X2 + 2
[active](X) = X
[isList](X) = 2.X + 2
[isNeList](X) = 2.X + 2
[isNePal](X) = 2.X
[isPal](X) = 2.X + 2
[isQid](X) = 2.X
[mark](X) = X
[a] = 2
[e] = 1
[fSNonEmpty] = 0
[i] = 2
[nil] = 1
[o] = 2
[tt] = 2
[u] = 2
[U11#](X) = 0
[U21#](X1,X2) = 0
[U22#](X) = 0
[U31#](X) = 0
[U41#](X1,X2) = 0
[U42#](X) = 0
[U51#](X1,X2) = 0
[U52#](X) = 0
[U61#](X) = 0
[U71#](X1,X2) = 0
[U72#](X) = 0
[U81#](X) = 0
[__#](X1,X2) = 0
[ACTIVE](X) = X + 2
[ISLIST](X) = 0
[ISNELIST](X) = 0
[ISNEPAL](X) = 0
[ISPAL](X) = 0
[ISQID](X) = 0
[MARK](X) = X + 2

Problem 1.19: 

SCC Processor:
-> Pairs:
 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S)))
 MARK(U11(X:S)) -> MARK(X:S)
 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S))
 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S)))
 MARK(U22(X:S)) -> MARK(X:S)
 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S)))
 MARK(U31(X:S)) -> MARK(X:S)
 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S))
 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S)))
 MARK(U42(X:S)) -> MARK(X:S)
 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S))
 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S)))
 MARK(U52(X:S)) -> MARK(X:S)
 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S)))
 MARK(U61(X:S)) -> MARK(X:S)
 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S))
 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S)))
 MARK(U72(X:S)) -> MARK(X:S)
 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S)))
 MARK(U81(X:S)) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 MARK(U11(X:S)) -> MARK(X:S)
 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U22(X:S)) -> MARK(X:S)
 MARK(U31(X:S)) -> MARK(X:S)
 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U42(X:S)) -> MARK(X:S)
 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U52(X:S)) -> MARK(X:S)
 MARK(U61(X:S)) -> MARK(X:S)
 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U72(X:S)) -> MARK(X:S)
 MARK(U81(X:S)) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
->->-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)

Problem 1.19: 

Subterm Processor:
-> Pairs:
 MARK(U11(X:S)) -> MARK(X:S)
 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U22(X:S)) -> MARK(X:S)
 MARK(U31(X:S)) -> MARK(X:S)
 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U42(X:S)) -> MARK(X:S)
 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U52(X:S)) -> MARK(X:S)
 MARK(U61(X:S)) -> MARK(X:S)
 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
 MARK(U72(X:S)) -> MARK(X:S)
 MARK(U81(X:S)) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Projection:
 pi(MARK) = 1

Problem 1.19: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S)
 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S)
 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S)
 U22(active(X:S)) -> U22(X:S)
 U22(mark(X:S)) -> U22(X:S)
 U31(active(X:S)) -> U31(X:S)
 U31(mark(X:S)) -> U31(X:S)
 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S)
 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S)
 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S)
 U42(active(X:S)) -> U42(X:S)
 U42(mark(X:S)) -> U42(X:S)
 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S)
 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S)
 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S)
 U52(active(X:S)) -> U52(X:S)
 U52(mark(X:S)) -> U52(X:S)
 U61(active(X:S)) -> U61(X:S)
 U61(mark(X:S)) -> U61(X:S)
 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S)
 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S)
 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S)
 U72(active(X:S)) -> U72(X:S)
 U72(mark(X:S)) -> U72(X:S)
 U81(active(X:S)) -> U81(X:S)
 U81(mark(X:S)) -> U81(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(tt)
 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
 active(U22(tt)) -> mark(tt)
 active(U31(tt)) -> mark(tt)
 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
 active(U42(tt)) -> mark(tt)
 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
 active(U52(tt)) -> mark(tt)
 active(U61(tt)) -> mark(tt)
 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
 active(U72(tt)) -> mark(tt)
 active(U81(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
 active(isList(nil)) -> mark(tt)
 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
 active(isPal(nil)) -> mark(tt)
 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
 active(isQid(a)) -> mark(tt)
 active(isQid(e)) -> mark(tt)
 active(isQid(i)) -> mark(tt)
 active(isQid(o)) -> mark(tt)
 active(isQid(u)) -> mark(tt)
 isList(active(X:S)) -> isList(X:S)
 isList(mark(X:S)) -> isList(X:S)
 isNeList(active(X:S)) -> isNeList(X:S)
 isNeList(mark(X:S)) -> isNeList(X:S)
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 isPal(active(X:S)) -> isPal(X:S)
 isPal(mark(X:S)) -> isPal(X:S)
 isQid(active(X:S)) -> isQid(X:S)
 isQid(mark(X:S)) -> isQid(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S))
 mark(U22(X:S)) -> active(U22(mark(X:S)))
 mark(U31(X:S)) -> active(U31(mark(X:S)))
 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S))
 mark(U42(X:S)) -> active(U42(mark(X:S)))
 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S))
 mark(U52(X:S)) -> active(U52(mark(X:S)))
 mark(U61(X:S)) -> active(U61(mark(X:S)))
 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S))
 mark(U72(X:S)) -> active(U72(mark(X:S)))
 mark(U81(X:S)) -> active(U81(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isList(X:S)) -> active(isList(X:S))
 mark(isNeList(X:S)) -> active(isNeList(X:S))
 mark(isNePal(X:S)) -> active(isNePal(X:S))
 mark(isPal(X:S)) -> active(isPal(X:S))
 mark(isQid(X:S)) -> active(isQid(X:S))
 mark(a) -> active(a)
 mark(e) -> active(e)
 mark(i) -> active(i)
 mark(nil) -> active(nil)
 mark(o) -> active(o)
 mark(tt) -> active(tt)
 mark(u) -> active(u)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.