YES

TRS:

  active(f(f(a()))) -> mark(c(f(g(f(a())))))
  active(f(X)) -> f(active(X))
  active(g(X)) -> g(active(X))
  f(mark(X)) -> mark(f(X))
  g(mark(X)) -> mark(g(X))
  proper(f(X)) -> f(proper(X))
  proper(a()) -> ok(a())
  proper(c(X)) -> c(proper(X))
  proper(g(X)) -> g(proper(X))
  f(ok(X)) -> ok(f(X))
  c(ok(X)) -> ok(c(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{18, -2 + x1}
  active#_A(x1) = max{2, 8 + x1}
  f_A(x1) = max{7, x1}
  f#_A(x1) = max{0, 13}
  a_A = 41
  a#_A = 14
  mark_A(x1) = max{38, 20 + x1}
  mark#_A(x1) = max{5, 12}
  c_A(x1) = max{19, -1}
  c#_A(x1) = max{8, 3}
  g_A(x1) = max{18, x1}
  g#_A(x1) = max{12, 6}
  proper_A(x1) = max{9, 1 + x1}
  proper#_A(x1) = max{21, 4}
  ok_A(x1) = max{19, -1 + x1}
  ok#_A(x1) = max{1, 7}
  top_A(x1) = max{0, 1}
  top#_A(x1) = max{20, 10 + x1}

precedence:

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