YES
Trs:
 {f(a()) -> f(b()),
  g(b()) -> g(a())}
 Comment:
  We consider a non-duplicating trs.
  BOUND:
   Automaton:
    {f_1(q9) -> q10,
     f_0(q4) -> q4,
       b_1() -> q9,
       b_0() -> q4,
       a_1() -> q5,
       a_0() -> q4,
     g_1(q5) -> q6,
     g_0(q4) -> q4,
         q10 -> q4,
          q6 -> q4}
   Strict:
   {}
   Qed