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

Proof:
 Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {3,2}
   transitions:
    a1(10) -> 11*
    b1(4) -> 5*
    b2(12) -> 13*
    a0(1) -> 2*
    b0(1) -> 1*
    c0(1) -> 3*
    1 -> 10,4
    5 -> 2*
    10 -> 12*
    11 -> 3*
    13 -> 11*
  problem:
   
  Qed