YES(?,O(n^1))

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

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