NO

Problem 1: 

(VAR v_NonEmpty:S IL:S L:S M:S N:S X:S)
(RULES
U11(tt) -> s(length(L:S))
U21(tt) -> nil
U31(tt) -> cons(N:S)
and(tt) -> X:S
isNat -> isNat
isNat -> isNatList
isNat -> tt
isNatIList -> and(isNat)
isNatIList -> isNatList
isNatIList -> tt
isNatList -> and(isNat)
isNatList -> tt
length(cons(N:S)) -> U11(and(isNatList))
length(nil) -> 0
take(0,IL:S) -> U21(isNatIList)
take(s(M:S),cons(N:S)) -> U31(and(isNatIList))
zeros -> cons(0)
)

Problem 1: 

Extra Variables Processor:
-> Rules:
 U11(tt) -> s(length(L:S))
 U21(tt) -> nil
 U31(tt) -> cons(N:S)
 and(tt) -> X:S
 isNat -> isNat
 isNat -> isNatList
 isNat -> tt
 isNatIList -> and(isNat)
 isNatIList -> isNatList
 isNatIList -> tt
 isNatList -> and(isNat)
 isNatList -> tt
 length(cons(N:S)) -> U11(and(isNatList))
 length(nil) -> 0
 take(0,IL:S) -> U21(isNatIList)
 take(s(M:S),cons(N:S)) -> U31(and(isNatIList))
 zeros -> cons(0)
-> The system has extra variables.

The problem is infinite.