YES(?,ELEMENTARY)

'epo* (timeout of 60.0 seconds)'
--------------------------------
Answer:           YES(?,ELEMENTARY)
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  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()))))}

Proof Output:    
  Strict Rules in Predicative Notation:
   {  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()))))}
  Safe Mapping:
   safe(filter) = {1, 2, 3}, safe(cons) = {1}, safe(0) = {},
   safe(s) = {1}, safe(sieve) = {1}, safe(nats) = {1},
   safe(zprimes) = {}
  Argument Permutation:
   mu(filter) = [3, 1, 2], mu(sieve) = [1], mu(nats) = [1],
   mu(zprimes) = []
  Precedence:
   zprimes ~ zprimes, zprimes > nats, zprimes > sieve,
   zprimes > filter, nats ~ nats, nats ~ sieve, nats > filter,
   sieve ~ nats, sieve ~ sieve, sieve > filter, filter ~ filter