NO

Problem 1: 

(VAR v_NonEmpty:S X:S XS:S)
(RULES
head(cons(X:S)) -> X:S
incr(cons(X:S)) -> cons(s(X:S))
nats -> cons(0)
odds -> incr(pairs)
pairs -> cons(0)
tail(cons(X:S)) -> XS:S
)

Problem 1: 

Extra Variables Processor:
-> Rules:
 head(cons(X:S)) -> X:S
 incr(cons(X:S)) -> cons(s(X:S))
 nats -> cons(0)
 odds -> incr(pairs)
 pairs -> cons(0)
 tail(cons(X:S)) -> XS:S
-> The system has extra variables.

The problem is infinite.