Problem:
 f(f(x)) -> f(x)
 g(0()) -> g(f(0()))

Proof:
 Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {3,2}
   transitions:
    g1(5) -> 6*
    f1(4) -> 5*
    01() -> 4*
    f0(1) -> 2*
    g0(1) -> 3*
    00() -> 1*
    6 -> 3*
  problem:
   
  Qed