NO

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

Proof:
 Nonconfluence Processor:
  terms: f(h(c(),c())) *<- f(c()) ->* c()
  Qed
  
  first automaton:
   final states: {9}
   transitions:
    c() -> 11,10
    h(11,10) -> 12*
    h(10,10) -> 11,10
    f(12) -> 9*
  
  second automaton:
   final states: {13}
   transitions:
    c() -> 13*
    h(13,13) -> 13*