YES(?,O(n^1))

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

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