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

Proof:
 Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {4,3,2}
   transitions:
    b1(7) -> 8*
    a1(5) -> 6*
    a1(6) -> 7*
    a0(1) -> 2*
    c0(1) -> 4*
    d0(1) -> 3*
    b0(1) -> 1*
    1 -> 5*
    8 -> 4*
  problem:
   
  Qed