NO

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

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