Problem:
 a() -> h(c())
 a() -> h(f(c()))
 h(x) -> h(h(x))
 f(x) -> f(g(x))

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