YES

TRS:

  active(f(f(a()))) -> mark(f(g(f(a()))))
  active(f(X)) -> f(active(X))
  f(mark(X)) -> mark(f(X))
  proper(f(X)) -> f(proper(X))
  proper(a()) -> ok(a())
  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{4, -3 + x1}
  active#_A(x1) = max{0, 23}
  f_A(x1) = max{2, x1}
  f#_A(x1) = max{6, 2}
  a_A = 25
  a#_A = 24
  mark_A(x1) = max{8, 6 + x1}
  mark#_A(x1) = max{1, -1}
  g_A(x1) = max{14, 16}
  g#_A(x1) = max{1, 5}
  proper_A(x1) = max{4, 1 + x1}
  proper#_A(x1) = max{16, 3}
  ok_A(x1) = max{15, -2 + x1}
  ok#_A(x1) = max{4, -1}
  top_A(x1) = max{0, 0}
  top#_A(x1) = max{13, 8 + x1}

precedence:

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