NO

Problem 1: 

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

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 FILTER(s(s(X:S)),cons(Y:S,Z:S)) -> FILTER(s(s(X:S)),Z:S)
 FILTER(s(s(X:S)),cons(Y:S,Z:S)) -> FILTER(X:S,sieve(Y:S))
 FILTER(s(s(X:S)),cons(Y:S,Z:S)) -> IF(divides(s(s(X:S)),Y:S),filter(s(s(X:S)),Z:S),cons(Y:S,filter(X:S,sieve(Y:S))))
 FILTER(s(s(X:S)),cons(Y:S,Z:S)) -> SIEVE(Y:S)
 FROM(X:S) -> FROM(s(X:S))
 PRIMES -> FROM(s(s(0)))
 PRIMES -> SIEVE(from(s(s(0))))
 SIEVE(cons(X:S,Y:S)) -> FILTER(X:S,sieve(Y:S))
 SIEVE(cons(X:S,Y:S)) -> SIEVE(Y:S)
-> Rules:
 filter(s(s(X:S)),cons(Y:S,Z:S)) -> if(divides(s(s(X:S)),Y:S),filter(s(s(X:S)),Z:S),cons(Y:S,filter(X:S,sieve(Y:S))))
 from(X:S) -> cons(X:S,from(s(X:S)))
 head(cons(X:S,Y:S)) -> X:S
 if(ffalse,X:S,Y:S) -> Y:S
 if(ttrue,X:S,Y:S) -> X:S
 primes -> sieve(from(s(s(0))))
 sieve(cons(X:S,Y:S)) -> cons(X:S,filter(X:S,sieve(Y:S)))
 tail(cons(X:S,Y:S)) -> Y:S

Problem 1: 

Infinite Processor:
-> Pairs:
 FILTER(s(s(X:S)),cons(Y:S,Z:S)) -> FILTER(s(s(X:S)),Z:S)
 FILTER(s(s(X:S)),cons(Y:S,Z:S)) -> FILTER(X:S,sieve(Y:S))
 FILTER(s(s(X:S)),cons(Y:S,Z:S)) -> IF(divides(s(s(X:S)),Y:S),filter(s(s(X:S)),Z:S),cons(Y:S,filter(X:S,sieve(Y:S))))
 FILTER(s(s(X:S)),cons(Y:S,Z:S)) -> SIEVE(Y:S)
 FROM(X:S) -> FROM(s(X:S))
 PRIMES -> FROM(s(s(0)))
 PRIMES -> SIEVE(from(s(s(0))))
 SIEVE(cons(X:S,Y:S)) -> FILTER(X:S,sieve(Y:S))
 SIEVE(cons(X:S,Y:S)) -> SIEVE(Y:S)
-> Rules:
 filter(s(s(X:S)),cons(Y:S,Z:S)) -> if(divides(s(s(X:S)),Y:S),filter(s(s(X:S)),Z:S),cons(Y:S,filter(X:S,sieve(Y:S))))
 from(X:S) -> cons(X:S,from(s(X:S)))
 head(cons(X:S,Y:S)) -> X:S
 if(ffalse,X:S,Y:S) -> Y:S
 if(ttrue,X:S,Y:S) -> X:S
 primes -> sieve(from(s(s(0))))
 sieve(cons(X:S,Y:S)) -> cons(X:S,filter(X:S,sieve(Y:S)))
 tail(cons(X:S,Y:S)) -> Y:S
-> Pairs in cycle:
 FROM(X:S) -> FROM(s(X:S))

The problem is infinite.