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

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