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

Proof:
 Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {3,2}
   transitions:
    b1(10) -> 11*
    c1(9) -> 10*
    a1(8) -> 9*
    a0(1) -> 2*
    b0(1) -> 1*
    c0(1) -> 3*
    1 -> 8,3,2
    8 -> 9*
    9 -> 10*
    11 -> 10,3
  problem:
   
  Qed