YES(?,O(n^1))

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

Proof:
 Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {4,3,2}
   transitions:
    d1(17) -> 18*
    d1(6) -> 7*
    b1(15) -> 16*
    b1(5) -> 6*
    b1(14) -> 15*
    a0(1) -> 2*
    d0(1) -> 1*
    b0(1) -> 3*
    c0(1) -> 4*
    1 -> 17,5
    6 -> 14*
    7 -> 2*
    16 -> 2*
    18 -> 4*
  problem:
   
  Qed