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

Proof:
 Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {3,2}
   transitions:
    a1(5) -> 6*
    b1(4) -> 5*
    c2(12) -> 13*
    c2(13) -> 14*
    b2(11) -> 12*
    a0(1) -> 2*
    a2(10) -> 11*
    b0(1) -> 3*
    c0(1) -> 1*
    1 -> 4,2
    4 -> 10*
    5 -> 6,3
    6 -> 12,5,3
    10 -> 11*
    14 -> 5*
  problem:
   
  Qed