Problem:
 a(x) -> b(x)
 a(x) -> c(c(x))
 b(x) -> g(b(x))
 c(x) -> c(x)

Proof:
 Nonconfluence Processor:
  terms: b(f4()) *<- a(f4()) ->* c(c(f4()))
  Qed
  
  first automaton:
   final states: {4}
   transitions:
    g(4) -> 4*
    b(5) -> 4*
    f4() -> 5*
  
  second automaton:
   final states: {1}
   transitions:
    f4() -> 2*
    c(2) -> 3*
    c(3) -> 1*