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

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