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

Proof:
 Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {3,2}
   transitions:
    b1(10) -> 11*
    a1(9) -> 10*
    a1(8) -> 9*
    b2(12) -> 13*
    a0(1) -> 2*
    b0(1) -> 3*
    c0(1) -> 1*
    1 -> 8*
    8 -> 12*
    11 -> 13,10,3
    13 -> 10*
  problem:
   
  Qed