NO

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

Proof:
 Nonconfluence Processor:
  terms: h(a(),a()) *<- h(a(),c()) ->* b()
  Qed
  
  first automaton:
   final states: {6}
   transitions:
    h(8,7) -> 6*
    a() -> 8,7
  
  second automaton:
   final states: {1}
   transitions:
    b() -> 1*
    f(1) -> 1*