NO

Problem:
 b() -> a()
 b() -> c()
 c() -> b()
 c() -> d()

Proof:
 Nonconfluence Processor:
  terms: d() *<- c() ->* a()
  Qed
  
  first automaton:
   final states: {1}
   transitions:
    d() -> 1*
  
  second automaton:
   final states: {3}
   transitions:
    a() -> 3*