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

Proof:
 Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {4,3,2}
   transitions:
    a1(13) -> 14*
    d1(9) -> 10*
    d1(11) -> 12*
    c1(10) -> 11*
    d2(21) -> 22*
    d2(23) -> 24*
    c2(22) -> 23*
    a0(1) -> 2*
    b0(1) -> 3*
    c0(1) -> 4*
    d0(1) -> 1*
    1 -> 13,9
    12 -> 2*
    13 -> 21*
    14 -> 23,11,4
    24 -> 14,4
  problem:
   
  Qed