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

Proof:
 Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {4,3,2}
   transitions:
    c1(12) -> 13*
    d1(11) -> 12*
    d1(6) -> 7*
    a1(5) -> 6*
    a0(1) -> 2*
    c0(1) -> 4*
    b0(1) -> 3*
    d0(1) -> 1*
    1 -> 11,4,5
    7 -> 3*
    12 -> 13,3
    13 -> 3*
  problem:
   
  Qed