YES
O(n)
TRS:
 {      g(a()) -> b(),
           a() -> g(c()),
  f(g(X), b()) -> f(a(), X)}
 DUP: We consider a non-duplicating system.
  Trs:
   {      g(a()) -> b(),
             a() -> g(c()),
    f(g(X), b()) -> f(a(), X)}
  BOUND:
   Automaton:
    {
     f_2(11, 10) -> 5,
      f_1(8, 10) -> 5,
       f_1(8, 6) -> 5,
       f_1(8, 5) -> 5,
       f_0(5, 5) -> 5,
           b_1() -> 5,
           b_0() -> 5,
           a_2() -> 11,
           a_1() -> 8,
           a_0() -> 5,
           c_3() -> 12,
           c_2() -> 10,
           c_1() -> 6,
           c_0() -> 5,
         g_3(12) -> 11,
         g_2(10) -> 8,
          g_1(6) -> 5,
          g_0(5) -> 5
    }
   Strict:
    {}
   Qed