Problem:
 f(1()) -> f(g(1()))
 f(f(x)) -> f(x)
 g(0()) -> g(f(0()))
 g(g(x)) -> g(x)

Proof:
 Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {4,3}
   transitions:
    g1(12) -> 13*
    g1(8) -> 9*
    f1(9) -> 10*
    f1(11) -> 12*
    01() -> 11*
    11() -> 8*
    f0(2) -> 3*
    f0(1) -> 3*
    10() -> 1*
    g0(2) -> 4*
    g0(1) -> 4*
    00() -> 2*
    10 -> 3*
    13 -> 4*
  problem:
   
  Qed