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

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