NO

Problem 1: 

(VAR v_NonEmpty:S N:S X:S XS:S Y:S)
(RULES
incr(cons(X:S)) -> cons(s(X:S))
oddNs -> incr(pairNs)
pairNs -> cons(0)
repItems(cons(X:S)) -> cons(X:S)
repItems(nil) -> nil
tail(cons(X:S)) -> XS:S
take(0,XS:S) -> nil
take(s(N:S),cons(X:S)) -> cons(X:S)
zip(cons(X:S),cons(Y:S)) -> cons(pair(X:S,Y:S))
zip(nil,XS:S) -> nil
zip(X:S,nil) -> nil
)

Problem 1: 

Extra Variables Processor:
-> Rules:
 incr(cons(X:S)) -> cons(s(X:S))
 oddNs -> incr(pairNs)
 pairNs -> cons(0)
 repItems(cons(X:S)) -> cons(X:S)
 repItems(nil) -> nil
 tail(cons(X:S)) -> XS:S
 take(0,XS:S) -> nil
 take(s(N:S),cons(X:S)) -> cons(X:S)
 zip(cons(X:S),cons(Y:S)) -> cons(pair(X:S,Y:S))
 zip(nil,XS:S) -> nil
 zip(X:S,nil) -> nil
-> The system has extra variables.

The problem is infinite.