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

Proof:
 Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {3,2}
   transitions:
    b1(6) -> 7*
    c1(5) -> 6*
    a1(4) -> 5*
    a0(1) -> 2*
    b0(1) -> 1*
    c0(1) -> 3*
    1 -> 4,2
    4 -> 5*
    7 -> 5,2
  problem:
   
  Qed