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{48, 23 + x1}
  active#_A(x1) = max{1, -3 + x1}
  f_A(x1) = max{51, 26 + x1}
  f#_A(x1) = max{22, -2 + x1}
  mark_A(x1) = max{53, 7 + x1}
  mark#_A(x1) = max{6, 7}
  g_A(x1) = max{43, 8 + x1}
  g#_A(x1) = max{41, -1}
  h_A(x1) = max{53, 7 + x1}
  h#_A(x1) = max{48, -4}
  proper_A(x1) = max{2, 1 + x1}
  proper#_A(x1) = max{49, 42 + x1}
  ok_A(x1) = max{95, 49 + x1}
  ok#_A(x1) = max{0, 40}
  top_A(x1) = max{0, 0}
  top#_A(x1) = max{39, 36 + x1}

precedence:

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