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

Proof:
 Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {3,2}
   transitions:
    b1(7) -> 8*
    c1(6) -> 7*
    a1(5) -> 6*
    a1(4) -> 5*
    b2(17) -> 18*
    a0(1) -> 2*
    c2(16) -> 17*
    b0(1) -> 1*
    a2(15) -> 16*
    a2(14) -> 15*
    c0(1) -> 3*
    1 -> 4,2
    4 -> 5*
    5 -> 6*
    7 -> 14*
    8 -> 5,2
    14 -> 15*
    15 -> 16*
    18 -> 6*
  problem:
   
  Qed