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

Proof:
 Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {3,2}
   transitions:
    a1(8) -> 9*
    b1(7) -> 8*
    c2(18) -> 19*
    b2(17) -> 18*
    a0(1) -> 2*
    a2(15) -> 16*
    a2(16) -> 17*
    b0(1) -> 3*
    c0(1) -> 1*
    1 -> 7,2
    7 -> 15*
    8 -> 9,3
    9 -> 18,8,3
    15 -> 16*
    16 -> 17*
    19 -> 8*
  problem:
   
  Qed