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

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