NO

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

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