Problem:
 half(0()) -> 0()
 half(s(0())) -> 0()
 half(s(s(x))) -> s(half(x))
 s(log(0())) -> s(0())
 log(s(x)) -> s(log(half(s(x))))

Proof:
 Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {4,3,2}
   transitions:
    01() -> 5*
    half0(1) -> 2*
    00() -> 1*
    s0(1) -> 3*
    log0(1) -> 4*
    5 -> 2*
  problem:
   
  Qed