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

Proof:
 Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {3,2}
   transitions:
    c1(7) -> 8*
    c1(8) -> 9*
    a1(5) -> 6*
    a1(6) -> 7*
    b1(4) -> 5*
    a0(1) -> 2*
    b0(1) -> 3*
    c0(1) -> 1*
    1 -> 4,2
    4 -> 6*
    5 -> 6*
    6 -> 7*
    9 -> 7,2
  problem:
   
  Qed