NO

Problem 1: 

(VAR v_NonEmpty:S X:S Y:S Z:S)
(RULES
U11(tt) -> U12(isNeList)
U12(tt) -> tt
U21(tt) -> U22(isList)
U22(tt) -> U23(isList)
U23(tt) -> tt
U31(tt) -> U32(isQid)
U32(tt) -> tt
U41(tt) -> U42(isList)
U42(tt) -> U43(isNeList)
U43(tt) -> tt
U51(tt) -> U52(isNeList)
U52(tt) -> U53(isList)
U53(tt) -> tt
U61(tt) -> U62(isQid)
U62(tt) -> tt
U71(tt) -> U72(isNePal)
U72(tt) -> tt
__(__(X:S,Y:S),Z:S) -> __(X:S,__(Y:S,Z:S))
__(nil,X:S) -> X:S
__(X:S,nil) -> X:S
and(tt) -> X:S
isList -> U11(isPalListKind)
isList -> U21(and(isPalListKind))
isList -> tt
isNeList -> U31(isPalListKind)
isNeList -> U41(and(isPalListKind))
isNeList -> U51(and(isPalListKind))
isNePal -> U61(isPalListKind)
isNePal -> and(and(isQid))
isPal -> U71(isPalListKind)
isPal -> tt
isPalListKind -> and(isPalListKind)
isPalListKind -> tt
isQid -> tt
)

Problem 1: 

Extra Variables Processor:
-> Rules:
 U11(tt) -> U12(isNeList)
 U12(tt) -> tt
 U21(tt) -> U22(isList)
 U22(tt) -> U23(isList)
 U23(tt) -> tt
 U31(tt) -> U32(isQid)
 U32(tt) -> tt
 U41(tt) -> U42(isList)
 U42(tt) -> U43(isNeList)
 U43(tt) -> tt
 U51(tt) -> U52(isNeList)
 U52(tt) -> U53(isList)
 U53(tt) -> tt
 U61(tt) -> U62(isQid)
 U62(tt) -> tt
 U71(tt) -> U72(isNePal)
 U72(tt) -> tt
 __(__(X:S,Y:S),Z:S) -> __(X:S,__(Y:S,Z:S))
 __(nil,X:S) -> X:S
 __(X:S,nil) -> X:S
 and(tt) -> X:S
 isList -> U11(isPalListKind)
 isList -> U21(and(isPalListKind))
 isList -> tt
 isNeList -> U31(isPalListKind)
 isNeList -> U41(and(isPalListKind))
 isNeList -> U51(and(isPalListKind))
 isNePal -> U61(isPalListKind)
 isNePal -> and(and(isQid))
 isPal -> U71(isPalListKind)
 isPal -> tt
 isPalListKind -> and(isPalListKind)
 isPalListKind -> tt
 isQid -> tt
-> The system has extra variables.

The problem is infinite.