Problem:
 a(x1) -> x1
 a(a(b(x1))) -> b(b(a(a(x1))))
 c(b(x1)) -> c(a(x1))

Proof:
 Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {3,2}
   transitions:
    c1(8) -> 9*
    a1(7) -> 8*
    a0(1) -> 2*
    b0(1) -> 1*
    c0(1) -> 3*
    1 -> 7,2
    7 -> 8*
    9 -> 3*
  problem:
   
  Qed