YES

TRS:

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

max/plus interpretations on N:

  active_A(x1) = max{1, -13}
  active#_A(x1) = max{0, 12 + x1}
  c_A = 22
  c#_A = 28
  mark_A(x1) = max{1, -13}
  mark#_A(x1) = max{27, 17 + x1}
  f_A(x1) = max{6, 8 + x1}
  f#_A(x1) = max{2, 26}
  g_A(x1) = max{8, -14 + x1}
  g#_A(x1) = max{5, 17}
  proper_A(x1) = max{3, 3 + x1}
  proper#_A(x1) = max{27, 27}
  ok_A(x1) = max{8, -1 + x1}
  ok#_A(x1) = max{15, 1}
  top_A(x1) = max{0, 1}
  top#_A(x1) = max{16, 13 + x1}

precedence:

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