YES(?,PRIMREC)

We are left with following problem, upon which TcT provides the
certificate YES(?,PRIMREC).

Strict Trs:
  { filter(cons(X), 0(), M) -> cons(0())
  , filter(cons(X), s(N), M) -> cons(X)
  , sieve(cons(0())) -> cons(0())
  , sieve(cons(s(N))) -> cons(s(N))
  , nats(N) -> cons(N)
  , zprimes() -> sieve(nats(s(s(0())))) }
Obligation:
  innermost runtime complexity
Answer:
  YES(?,PRIMREC)

The input was oriented with the instance of'multiset path order' as
induced by the precedence

 filter > 0, cons > 0, s > filter, s > cons, s > 0, sieve > filter,
 sieve > cons, sieve > 0, nats > filter, nats > cons, nats > 0,
 zprimes > filter, zprimes > cons, zprimes > 0, zprimes > s,
 zprimes > sieve, zprimes > nats, filter ~ cons, s ~ sieve,
 s ~ nats, sieve ~ nats .

Hurray, we answered YES(?,PRIMREC)