NO

Problem 1: 

(VAR v_NonEmpty:S X:S Y:S Z:S)
(RULES
U11(tt) -> tt
U21(tt) -> U22(isList)
U22(tt) -> tt
U31(tt) -> tt
U41(tt) -> U42(isNeList)
U42(tt) -> tt
U51(tt) -> U52(isList)
U52(tt) -> tt
U61(tt) -> tt
U71(tt) -> U72(isPal)
U72(tt) -> tt
U81(tt) -> tt
__(__(X:S,Y:S),Z:S) -> __(X:S,__(Y:S,Z:S))
__(nil,X:S) -> X:S
__(X:S,nil) -> X:S
isList -> U11(isNeList)
isList -> U21(isList)
isList -> tt
isNeList -> U31(isQid)
isNeList -> U41(isList)
isNeList -> U51(isNeList)
isNePal -> U61(isQid)
isNePal -> U71(isQid)
isPal -> U81(isNePal)
isPal -> tt
isQid -> tt
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 U21#(tt) -> U22#(isList)
 U21#(tt) -> ISLIST
 U41#(tt) -> U42#(isNeList)
 U41#(tt) -> ISNELIST
 U51#(tt) -> U52#(isList)
 U51#(tt) -> ISLIST
 U71#(tt) -> U72#(isPal)
 U71#(tt) -> ISPAL
 __#(__(X:S,Y:S),Z:S) -> __#(X:S,__(Y:S,Z:S))
 __#(__(X:S,Y:S),Z:S) -> __#(Y:S,Z:S)
 ISLIST -> U11#(isNeList)
 ISLIST -> U21#(isList)
 ISLIST -> ISLIST
 ISLIST -> ISNELIST
 ISNELIST -> U31#(isQid)
 ISNELIST -> U41#(isList)
 ISNELIST -> U51#(isNeList)
 ISNELIST -> ISLIST
 ISNELIST -> ISNELIST
 ISNELIST -> ISQID
 ISNEPAL -> U61#(isQid)
 ISNEPAL -> U71#(isQid)
 ISNEPAL -> ISQID
 ISPAL -> U81#(isNePal)
 ISPAL -> ISNEPAL
-> Rules:
 U11(tt) -> tt
 U21(tt) -> U22(isList)
 U22(tt) -> tt
 U31(tt) -> tt
 U41(tt) -> U42(isNeList)
 U42(tt) -> tt
 U51(tt) -> U52(isList)
 U52(tt) -> tt
 U61(tt) -> tt
 U71(tt) -> U72(isPal)
 U72(tt) -> tt
 U81(tt) -> tt
 __(__(X:S,Y:S),Z:S) -> __(X:S,__(Y:S,Z:S))
 __(nil,X:S) -> X:S
 __(X:S,nil) -> X:S
 isList -> U11(isNeList)
 isList -> U21(isList)
 isList -> tt
 isNeList -> U31(isQid)
 isNeList -> U41(isList)
 isNeList -> U51(isNeList)
 isNePal -> U61(isQid)
 isNePal -> U71(isQid)
 isPal -> U81(isNePal)
 isPal -> tt
 isQid -> tt

Problem 1: 

Infinite Processor:
-> Pairs:
 U21#(tt) -> U22#(isList)
 U21#(tt) -> ISLIST
 U41#(tt) -> U42#(isNeList)
 U41#(tt) -> ISNELIST
 U51#(tt) -> U52#(isList)
 U51#(tt) -> ISLIST
 U71#(tt) -> U72#(isPal)
 U71#(tt) -> ISPAL
 __#(__(X:S,Y:S),Z:S) -> __#(X:S,__(Y:S,Z:S))
 __#(__(X:S,Y:S),Z:S) -> __#(Y:S,Z:S)
 ISLIST -> U11#(isNeList)
 ISLIST -> U21#(isList)
 ISLIST -> ISLIST
 ISLIST -> ISNELIST
 ISNELIST -> U31#(isQid)
 ISNELIST -> U41#(isList)
 ISNELIST -> U51#(isNeList)
 ISNELIST -> ISLIST
 ISNELIST -> ISNELIST
 ISNELIST -> ISQID
 ISNEPAL -> U61#(isQid)
 ISNEPAL -> U71#(isQid)
 ISNEPAL -> ISQID
 ISPAL -> U81#(isNePal)
 ISPAL -> ISNEPAL
-> Rules:
 U11(tt) -> tt
 U21(tt) -> U22(isList)
 U22(tt) -> tt
 U31(tt) -> tt
 U41(tt) -> U42(isNeList)
 U42(tt) -> tt
 U51(tt) -> U52(isList)
 U52(tt) -> tt
 U61(tt) -> tt
 U71(tt) -> U72(isPal)
 U72(tt) -> tt
 U81(tt) -> tt
 __(__(X:S,Y:S),Z:S) -> __(X:S,__(Y:S,Z:S))
 __(nil,X:S) -> X:S
 __(X:S,nil) -> X:S
 isList -> U11(isNeList)
 isList -> U21(isList)
 isList -> tt
 isNeList -> U31(isQid)
 isNeList -> U41(isList)
 isNeList -> U51(isNeList)
 isNePal -> U61(isQid)
 isNePal -> U71(isQid)
 isPal -> U81(isNePal)
 isPal -> tt
 isQid -> tt
-> Pairs in cycle:
 ISLIST -> ISLIST
 ISNELIST -> ISNELIST

The problem is infinite.