YES(?,O(n^1))

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

Proof:
 Bounds Processor:
  bound: 0
  enrichment: match
  automaton:
   final states: {4,3}
   transitions:
    a0(2) -> 3*
    a0(1) -> 3*
    b0(2) -> 1*
    b0(1) -> 1*
    d0(2) -> 2*
    d0(1) -> 2*
    c0(2) -> 4*
    c0(1) -> 4*
  problem:
   
  Qed