YES

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

Proof:
 WPO Processor:
  algebra: Sum
  weight function:
   w0 = 0
   w(d) = 3
   w(b) = w(a) = 2
   w(c) = 1
  status function:
   st(b) = st(d) = st(c) = st(a) = [0]
  precedence:
   c > b > a > d
  problem:
   
  Qed