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

Proof:
 Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {3,2}
   transitions:
    c1(12) -> 13*
    c1(14) -> 15*
    c1(13) -> 14*
    b1(11) -> 12*
    a1(10) -> 11*
    a0(1) -> 2*
    b0(1) -> 3*
    c0(1) -> 1*
    1 -> 10,3,2
    10 -> 11*
    11 -> 12*
    15 -> 12,3
  problem:
   
  Qed