YES

TRS:

  active(g(X)) -> mark(h(X))
  active(c()) -> mark(d())
  active(h(d())) -> mark(g(c()))
  proper(g(X)) -> g(proper(X))
  proper(h(X)) -> h(proper(X))
  proper(c()) -> ok(c())
  proper(d()) -> ok(d())
  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{6, -2 + x1}
  active#_A(x1) = max{1, 36 + x1}
  g_A(x1) = max{21, -3}
  g#_A(x1) = max{22, 24}
  mark_A(x1) = max{7, -14 + x1}
  mark#_A(x1) = max{47, 45 + x1}
  h_A(x1) = max{7, 9}
  h#_A(x1) = max{22, -1}
  c_A = 34
  c#_A = 22
  d_A = 24
  d#_A = 67
  proper_A(x1) = max{1, 2 + x1}
  proper#_A(x1) = max{46, 25}
  ok_A(x1) = max{9, -1 + x1}
  ok#_A(x1) = max{0, 2 + x1}
  top_A(x1) = max{0, 0}
  top#_A(x1) = max{47, 42 + x1}

precedence:

  g > active > mark > top > proper > h > c = ok > d