YES

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:
 WPO Processor:
  algebra: Sum
  weight function:
   w0 = 0
   w(b) = 4
   w(d) = w(r) = w(a) = 0
  status function:
   st(d) = st(r) = st(a) = st(b) = [0]
  precedence:
   r > d > a > b
  problem:
   
  Qed