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

Proof:
 Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {4,3,2}
   transitions:
    a1(11) -> 12*
    b1(9) -> 10*
    b1(8) -> 9*
    b0(1) -> 2*
    a0(1) -> 3*
    d0(1) -> 4*
    c0(1) -> 1*
    1 -> 11,8
    10 -> 12,4,3
    12 -> 4*
  problem:
   
  Qed