Problem:
 f(x,x) -> x
 f(x,e()) -> x
 f(e(),x) -> x
 f(x,i(x)) -> e()
 f(i(x),x) -> e()

Proof:
 Nonconfluence Processor:
  terms: e() *<- f(i(e()),e()) ->* i(e())
  Qed
  
  first automaton:
   final states: {1}
   transitions:
    e() -> 1*
  
  second automaton:
   final states: {2}
   transitions:
    e() -> 3*
    i(3) -> 2*