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))

linear polynomial interpretations on N:

  active_A(x1) = x1
  active#_A(x1) = x1
  c_A = 6
  c#_A = 5
  mark_A(x1) = x1 + 1
  mark#_A(x1) = x1 + 2
  f_A(x1) = 3
  f#_A(x1) = 5
  g_A(x1) = 0
  g#_A(x1) = 2
  proper_A(x1) = x1
  proper#_A(x1) = 8
  ok_A(x1) = x1
  ok#_A(x1) = x1 + 1
  top_A(x1) = x1
  top#_A(x1) = x1 + 8

precedence:

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