YES

TRS:

  active(f(X)) -> mark(g(h(f(X))))
  active(f(X)) -> f(active(X))
  active(h(X)) -> h(active(X))
  f(mark(X)) -> mark(f(X))
  h(mark(X)) -> mark(h(X))
  proper(f(X)) -> f(proper(X))
  proper(g(X)) -> g(proper(X))
  proper(h(X)) -> h(proper(X))
  f(ok(X)) -> ok(f(X))
  g(ok(X)) -> ok(g(X))
  h(ok(X)) -> ok(h(X))
  top(mark(X)) -> top(proper(X))
  top(ok(X)) -> top(active(X))

max/plus interpretations on N:

  active_A(x1) = max{5, 11 + x1}
  active#_A(x1) = max{5, 11 + x1}
  f_A(x1) = max{4, 37 + x1}
  f#_A(x1) = max{4, 37 + x1}
  mark_A(x1) = max{26, 5 + x1}
  mark#_A(x1) = max{26, 5 + x1}
  g_A(x1) = max{2, 1 + x1}
  g#_A(x1) = max{2, 1 + x1}
  h_A(x1) = max{16, 4 + x1}
  h#_A(x1) = max{16, 4 + x1}
  proper_A(x1) = max{3, 3 + x1}
  proper#_A(x1) = max{3, 3 + x1}
  ok_A(x1) = max{48, 36 + x1}
  ok#_A(x1) = max{48, 36 + x1}
  top_A(x1) = max{49, 24 + x1}
  top#_A(x1) = max{49, 24 + x1}

precedence:

  top > active > f = proper > g = h = ok > mark