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

Proof:
 Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {3}
   transitions:
    b1(20) -> 21*
    b1(10) -> 11*
    a1(12) -> 13*
    a1(9) -> 10*
    a1(8) -> 9*
    c1(19) -> 20*
    a0(2) -> 3*
    a0(1) -> 3*
    b0(2) -> 1*
    b0(1) -> 1*
    c0(2) -> 2*
    c0(1) -> 2*
    1 -> 12*
    2 -> 8*
    9 -> 19*
    11 -> 9,3
    13 -> 9*
    21 -> 9*
  problem:
   
  Qed