NO

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

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