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

Proof:
 Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {4,3}
   transitions:
    01() -> 6*
    f1(8) -> 9*
    g1(15) -> 16*
    g1(7) -> 8*
    02() -> 17*
    g0(2) -> 3*
    g0(1) -> 3*
    00() -> 1*
    s0(2) -> 2*
    s0(1) -> 2*
    f0(2) -> 4*
    f0(1) -> 4*
    1 -> 15*
    2 -> 7*
    6 -> 16,8,4,3
    9 -> 8,3
    16 -> 8*
    17 -> 9,3,8
  problem:
   
  Qed