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

Proof:
 Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {5,4,3}
   transitions:
    b1(20) -> 21*
    b1(10) -> 11*
    b1(7) -> 8*
    b1(9) -> 10*
    b1(6) -> 7*
    b1(23) -> 24*
    d1(30) -> 31*
    d1(22) -> 23*
    f1(8) -> 9*
    a0(2) -> 3*
    a0(1) -> 3*
    d0(2) -> 5*
    d0(1) -> 5*
    b0(2) -> 4*
    b0(1) -> 4*
    c0(2) -> 1*
    c0(1) -> 1*
    f0(2) -> 2*
    f0(1) -> 2*
    1 -> 30,6
    2 -> 22,20
    11 -> 3*
    21 -> 7*
    24 -> 23,5
    31 -> 23*
  problem:
   
  Qed