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

Proof:
 Nonconfluence Processor:
  terms: a() *<- g(g(b())) ->* b()
  Qed
  
  first automaton:
   final states: {2}
   transitions:
    a() -> 2*
    g(2) -> 2*
  
  second automaton:
   final states: {1}
   transitions:
    b() -> 1*