Problem:
 a() -> a()
 a() -> b()
 f(b(),b()) -> f(a(),b())
 f(x,a()) -> f(a(),b())

Proof:
 Nonconfluence Processor:
  terms: f(f3(),b()) *<- f(f3(),a()) ->* f(a(),b())
  Qed
  
  first automaton:
   final states: {1}
   transitions:
    f3() -> 3*
    b() -> 2*
    f(3,2) -> 1*
  
  second automaton:
   final states: {4}
   transitions:
    a() -> 6*
    b() -> 6,5
    f(6,5) -> 4*