NO

Problem 1: 

(VAR v_NonEmpty:S X:S Y:S Z:S)
(RULES
__(__(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 -> and(isList)
isList -> isNeList
isList -> tt
isNeList -> and(isList)
isNeList -> and(isNeList)
isNeList -> isQid
isNePal -> and(isQid)
isNePal -> isQid
isPal -> isNePal
isPal -> tt
isQid -> tt
)

Problem 1: 

Extra Variables Processor:
-> Rules:
 __(__(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 -> and(isList)
 isList -> isNeList
 isList -> tt
 isNeList -> and(isList)
 isNeList -> and(isNeList)
 isNeList -> isQid
 isNePal -> and(isQid)
 isNePal -> isQid
 isPal -> isNePal
 isPal -> tt
 isQid -> tt
-> The system has extra variables.

The problem is infinite.