NO

Problem 1: 

(VAR v_NonEmpty:S X:S Y:S)
(RULES
filter(s(s(X:S)),cons(Y:S)) -> if(divides(s(s(X:S)),Y:S))
from(X:S) -> cons(X:S)
head(cons(X:S)) -> X:S
if(ffalse) -> Y:S
if(ttrue) -> X:S
primes -> sieve(from(s(s(0))))
sieve(cons(X:S)) -> cons(X:S)
tail(cons(X:S)) -> Y:S
)

Problem 1: 

Extra Variables Processor:
-> Rules:
 filter(s(s(X:S)),cons(Y:S)) -> if(divides(s(s(X:S)),Y:S))
 from(X:S) -> cons(X:S)
 head(cons(X:S)) -> X:S
 if(ffalse) -> Y:S
 if(ttrue) -> X:S
 primes -> sieve(from(s(s(0))))
 sieve(cons(X:S)) -> cons(X:S)
 tail(cons(X:S)) -> Y:S
-> The system has extra variables.

The problem is infinite.