NO

Problem:
 a() -> a()
 g(g(a())) -> b()
 g(g(x)) -> g(g(g(b())))

Proof:
 Nonconfluence Processor:
  terms: b() *<- g(g(a())) ->* g(g(g(b())))
  Qed
  
  first automaton:
   final states: {10}
   transitions:
    b() -> 10*
  
  second automaton:
   final states: {6}
   transitions:
    g(8) -> 9*
    g(9) -> 9,6
    g(7) -> 8*
    b() -> 7*