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()

max/plus interpretations on N:

  a__filter_A(x1,x2,x3) = max{8, x1, x2, x3}
  a__filter#_A(x1,x2,x3) = max{8, x1, x2, x3}
  cons_A(x1,x2) = max{6, 3 + x1, x2}
  cons#_A(x1,x2) = max{6, 3 + x1, x2}
  0_A = 4
  0#_A = 4
  filter_A(x1,x2,x3) = max{8, x1, x2, x3}
  filter#_A(x1,x2,x3) = max{8, x1, x2, x3}
  s_A(x1) = max{0, x1}
  s#_A(x1) = max{0, x1}
  mark_A(x1) = max{0, x1}
  mark#_A(x1) = max{0, x1}
  a__sieve_A(x1) = max{14, 6 + x1}
  a__sieve#_A(x1) = max{14, 6 + x1}
  sieve_A(x1) = max{14, 6 + x1}
  sieve#_A(x1) = max{14, 6 + x1}
  a__nats_A(x1) = max{7, 8 + x1}
  a__nats#_A(x1) = max{7, 8 + x1}
  nats_A(x1) = max{8, 8 + x1}
  nats#_A(x1) = max{8, 8 + x1}
  a__zprimes_A = 19
  a__zprimes#_A = 19
  zprimes_A = 19
  zprimes#_A = 19

precedence:

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