YES

TRS:

  a__filter(cons(X,Y),0(),M) -> cons(0(),filter(Y,M,M))
  a__filter(cons(X,Y),s(N),M) -> cons(mark(X),filter(Y,N,M))
  a__sieve(cons(0(),Y)) -> cons(0(),sieve(Y))
  a__sieve(cons(s(N),Y)) -> cons(s(mark(N)),sieve(filter(Y,N,N)))
  a__nats(N) -> cons(mark(N),nats(s(N)))
  a__zprimes() -> a__sieve(a__nats(s(s(0()))))
  mark(filter(X1,X2,X3)) -> a__filter(mark(X1),mark(X2),mark(X3))
  mark(sieve(X)) -> a__sieve(mark(X))
  mark(nats(X)) -> a__nats(mark(X))
  mark(zprimes()) -> a__zprimes()
  mark(cons(X1,X2)) -> cons(mark(X1),X2)
  mark(0()) -> 0()
  mark(s(X)) -> s(mark(X))
  a__filter(X1,X2,X3) -> filter(X1,X2,X3)
  a__sieve(X) -> sieve(X)
  a__nats(X) -> nats(X)
  a__zprimes() -> zprimes()

linear polynomial interpretations on N:

  a__filter_A(x1,x2,x3) = x1 + x2 + x3 + 2
  a__filter#_A(x1,x2,x3) = x1 + x2 + 3
  cons_A(x1,x2) = x1 + 1
  cons#_A(x1,x2) = 0
  0_A = 1
  0#_A = 4
  filter_A(x1,x2,x3) = x1 + x2 + x3 + 2
  filter#_A(x1,x2,x3) = 1
  s_A(x1) = x1 + 1
  s#_A(x1) = x1 + 2
  mark_A(x1) = x1
  mark#_A(x1) = x1 + 2
  a__sieve_A(x1) = x1 + 3
  a__sieve#_A(x1) = x1 + 4
  sieve_A(x1) = x1 + 3
  sieve#_A(x1) = 3
  a__nats_A(x1) = x1 + 4
  a__nats#_A(x1) = x1 + 5
  nats_A(x1) = x1 + 4
  nats#_A(x1) = x1 + 3
  a__zprimes_A = 11
  a__zprimes#_A = 12
  zprimes_A = 11
  zprimes#_A = 0

precedence:

  a__sieve = nats > mark > a__filter > cons > 0 = filter = sieve > a__zprimes > s = zprimes > a__nats