YES(?,O(n^1))

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

Proof:
 Bounds Processor:
  bound: 3
  enrichment: match
  automaton:
   final states: {4,3,2}
   transitions:
    a1(17) -> 18*
    d1(11) -> 12*
    b1(9) -> 10*
    r1(8) -> 9*
    a2(25) -> 26*
    a0(1) -> 2*
    d2(19) -> 20*
    b0(1) -> 1*
    a3(29) -> 30*
    r0(1) -> 3*
    d0(1) -> 4*
    1 -> 17,11,8
    8 -> 19*
    10 -> 30,20,26,12,18,4,2
    11 -> 25*
    12 -> 3*
    18 -> 4*
    19 -> 29*
    20 -> 9*
    26 -> 12,3
    30 -> 20,9
  problem:
   
  Qed