YES

TRS:

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

max/plus interpretations on N:

  active_A(x1) = max{23, x1}
  active#_A(x1) = max{51, 2 + x1}
  filter_A(x1,x2,x3) = max{8, 99 + x1, 40 + x2, 62 + x3}
  filter#_A(x1,x2,x3) = max{88, 65, 18, 56}
  cons_A(x1,x2) = max{1, 7 + x1, 7}
  cons#_A(x1,x2) = max{19, 56, 19}
  0_A = 7
  0#_A = 0
  mark_A(x1) = max{11, 16 + x1}
  mark#_A(x1) = max{54, 49 + x1}
  s_A(x1) = max{93, 130 + x1}
  s#_A(x1) = max{48, -1}
  sieve_A(x1) = max{53, 47 + x1}
  sieve#_A(x1) = max{52, 1}
  nats_A(x1) = max{55, 87 + x1}
  nats#_A(x1) = max{0, 1}
  zprimes_A = 449
  zprimes#_A = 53

precedence:

  active = zprimes > filter = nats > mark > sieve > cons > 0 = s