YES

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

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [a](x0) = x0 + 8,
   
   [c](x0) = 2x0 + 1,
   
   [d](x0) = 2x0,
   
   [b](x0) = x0 + 2
  orientation:
   a(a(d(d(x1)))) = 4x1 + 16 >= 4x1 + 16 = d(d(b(b(x1))))
   
   a(a(x1)) = x1 + 16 >= x1 + 12 = b(b(b(b(b(b(x1))))))
   
   b(b(d(d(b(b(x1)))))) = 4x1 + 20 >= 4x1 + 19 = a(a(c(c(x1))))
   
   c(c(x1)) = 4x1 + 3 >= 4x1 = d(d(x1))
  problem:
   a(a(d(d(x1)))) -> d(d(b(b(x1))))
  KBO Processor:
   weight function:
    w0 = 1
    w(a) = w(d) = 1
    w(b) = 0
   precedence:
    b > d > a
   problem:
    
   Qed