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

Proof:
 Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {4,3}
   transitions:
    g1(15) -> 16*
    f1(5) -> 6*
    f1(14) -> 15*
    f1(11) -> 12*
    s1(13) -> 14*
    01() -> 13*
    f2(23) -> 24*
    f0(2) -> 3*
    f0(1) -> 3*
    s0(2) -> 1*
    s0(1) -> 1*
    g0(2) -> 4*
    g0(1) -> 4*
    00() -> 2*
    1 -> 11*
    2 -> 5*
    6 -> 12,3
    12 -> 3*
    13 -> 23*
    16 -> 4*
    24 -> 15*
  problem:
   
  Qed