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

Proof:
 Bounds Processor:
  bound: 3
  enrichment: match
  automaton:
   final states: {3,2}
   transitions:
    c3(34) -> 35*
    b1(4) -> 5*
    b3(30) -> 31*
    a1(12) -> 13*
    c1(10) -> 11*
    c2(22) -> 23*
    a0(1) -> 2*
    b2(18) -> 19*
    b0(1) -> 1*
    a2(26) -> 27*
    c0(1) -> 3*
    1 -> 10,4
    5 -> 27,23,13,4,2
    10 -> 26*
    11 -> 12,2
    12 -> 22,18
    13 -> 4*
    19 -> 13,4
    23 -> 13,4
    26 -> 34,30
    27 -> 23,13
    31 -> 27,23
    35 -> 27,23
  problem:
   
  Qed