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

Proof:
 Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {3,2}
   transitions:
    a1(8) -> 9*
    c1(7) -> 8*
    b2(13) -> 14*
    c2(12) -> 13*
    a0(1) -> 2*
    a2(20) -> 21*
    a2(10) -> 11*
    a2(11) -> 12*
    b0(1) -> 1*
    c0(1) -> 3*
    1 -> 21,12,11,7,2
    7 -> 10*
    9 -> 13,8,3
    12 -> 20*
    13 -> 9*
    14 -> 9,3
    21 -> 11*
  problem:
   
  Qed