YES

TRS:

  filter(cons(X,Y),0(),M) -> cons(0(),n__filter(activate(Y),M,M))
  filter(cons(X,Y),s(N),M) -> cons(X,n__filter(activate(Y),N,M))
  sieve(cons(0(),Y)) -> cons(0(),n__sieve(activate(Y)))
  sieve(cons(s(N),Y)) -> cons(s(N),n__sieve(filter(activate(Y),N,N)))
  nats(N) -> cons(N,n__nats(s(N)))
  zprimes() -> sieve(nats(s(s(0()))))
  filter(X1,X2,X3) -> n__filter(X1,X2,X3)
  sieve(X) -> n__sieve(X)
  nats(X) -> n__nats(X)
  activate(n__filter(X1,X2,X3)) -> filter(X1,X2,X3)
  activate(n__sieve(X)) -> sieve(X)
  activate(n__nats(X)) -> nats(X)
  activate(X) -> X

max/plus interpretations on N:

  filter_A(x1,x2,x3) = max{18, x1, 1 + x2, 2 + x3}
  filter#_A(x1,x2,x3) = max{18, x1, 1 + x2, 2 + x3}
  cons_A(x1,x2) = max{17, 3 + x1, x2}
  cons#_A(x1,x2) = max{17, 3 + x1, x2}
  0_A = 4
  0#_A = 4
  n__filter_A(x1,x2,x3) = max{18, x1, 1 + x2, 2 + x3}
  n__filter#_A(x1,x2,x3) = max{18, x1, 1 + x2, 2 + x3}
  activate_A(x1) = max{8, x1}
  activate#_A(x1) = max{8, x1}
  s_A(x1) = max{8, x1}
  s#_A(x1) = max{8, x1}
  sieve_A(x1) = max{35, 16 + x1}
  sieve#_A(x1) = max{35, 16 + x1}
  n__sieve_A(x1) = max{35, 16 + x1}
  n__sieve#_A(x1) = max{35, 16 + x1}
  nats_A(x1) = max{17, 9 + x1}
  nats#_A(x1) = max{17, 9 + x1}
  n__nats_A(x1) = max{17, 9 + x1}
  n__nats#_A(x1) = max{17, 9 + x1}
  zprimes_A = 36
  zprimes#_A = 36

precedence:

  zprimes > filter = activate = sieve > n__filter = nats > cons = n__nats > 0 = s = n__sieve