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

Proof:
 Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {3,2}
   transitions:
    b1(8) -> 9*
    a1(5) -> 6*
    a1(7) -> 8*
    a1(4) -> 5*
    c1(6) -> 7*
    b2(26) -> 27*
    a0(1) -> 2*
    a2(25) -> 26*
    a2(22) -> 23*
    a2(23) -> 24*
    b0(1) -> 1*
    c2(24) -> 25*
    c0(1) -> 3*
    1 -> 4,2
    4 -> 5*
    5 -> 6*
    7 -> 8*
    8 -> 22*
    9 -> 5,2
    22 -> 23*
    23 -> 24*
    25 -> 26*
    27 -> 6*
  problem:
   
  Qed