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

Proof:
 Bounds Processor:
  bound: 3
  enrichment: match
  automaton:
   final states: {3,2}
   transitions:
    c1(10) -> 11*
    c1(9) -> 10*
    b1(8) -> 9*
    a1(6) -> 7*
    a2(18) -> 19*
    a0(1) -> 2*
    b2(22) -> 23*
    b0(1) -> 3*
    a3(24) -> 25*
    c0(1) -> 1*
    1 -> 6,2
    6 -> 22,7,8
    7 -> 8,3
    8 -> 18*
    11 -> 23,19,9,3
    18 -> 19*
    19 -> 9*
    22 -> 24*
    23 -> 19,9
    24 -> 25*
    25 -> 23,19
  problem:
   
  Qed