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

Proof:
 Nonconfluence Processor:
  terms: f(a(),a()) *<- a() ->* f(b(),f(a(),a()))
  Qed
  
  first automaton:
   final states: {14}
   transitions:
    a() -> 16,15
    f(148,14) -> 15,16
    f(16,15) -> 14*
    f(15,15) -> 15,16
    b() -> 148*
  
  second automaton:
   final states: {9}
   transitions:
    a() -> 11,10
    f(13,10) -> 11,10
    f(11,10) -> 12*
    f(10,10) -> 11,10
    f(13,12) -> 9*
    b() -> 12,10,11,13