YES

TRS:

  active(f(f(X))) -> mark(c(f(g(f(X)))))
  active(c(X)) -> mark(d(X))
  active(h(X)) -> mark(c(d(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(c(X)) -> c(proper(X))
  proper(g(X)) -> g(proper(X))
  proper(d(X)) -> d(proper(X))
  proper(h(X)) -> h(proper(X))
  f(ok(X)) -> ok(f(X))
  c(ok(X)) -> ok(c(X))
  g(ok(X)) -> ok(g(X))
  d(ok(X)) -> ok(d(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{46, 68 + x1}
  active#_A(x1) = max{46, 68 + x1}
  f_A(x1) = max{0, 3 + x1}
  f#_A(x1) = max{0, 3 + x1}
  mark_A(x1) = max{72, 42 + x1}
  mark#_A(x1) = max{72, 42 + x1}
  c_A(x1) = max{5, 8 + x1}
  c#_A(x1) = max{5, 8 + x1}
  g_A(x1) = max{14, 14 + x1}
  g#_A(x1) = max{14, 14 + x1}
  d_A(x1) = max{9, 12 + x1}
  d#_A(x1) = max{9, 12 + x1}
  h_A(x1) = max{18, 41 + x1}
  h#_A(x1) = max{18, 41 + x1}
  proper_A(x1) = max{13, 15 + x1}
  proper#_A(x1) = max{13, 15 + x1}
  ok_A(x1) = max{71, 95 + x1}
  ok#_A(x1) = max{71, 95 + x1}
  top_A(x1) = max{96, 26 + x1}
  top#_A(x1) = max{96, 26 + x1}

precedence:

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