YES

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

Proof:
 DP Processor:
  DPs:
   d#(a(x1)) -> d#(x1)
   d#(a(x1)) -> b#(d(x1))
   c#(d(c(x1))) -> d#(x1)
   b#(d(d(x1))) -> c#(x1)
   b#(d(d(x1))) -> d#(c(x1))
   b#(d(d(x1))) -> d#(d(c(x1)))
   b#(d(d(x1))) -> c#(d(d(c(x1))))
   b#(d(d(x1))) -> c#(c(d(d(c(x1)))))
  TRS:
   d(a(x1)) -> b(d(x1))
   b(x1) -> a(a(a(x1)))
   c(d(c(x1))) -> a(d(x1))
   b(d(d(x1))) -> c(c(d(d(c(x1)))))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [c#](x0) = x0 + 11,
    
    [b#](x0) = x0 + 31,
    
    [d#](x0) = 4x0 + 14,
    
    [c](x0) = x0 + 1,
    
    [b](x0) = x0 + 19,
    
    [d](x0) = 4x0,
    
    [a](x0) = x0 + 5
   orientation:
    d#(a(x1)) = 4x1 + 34 >= 4x1 + 14 = d#(x1)
    
    d#(a(x1)) = 4x1 + 34 >= 4x1 + 31 = b#(d(x1))
    
    c#(d(c(x1))) = 4x1 + 15 >= 4x1 + 14 = d#(x1)
    
    b#(d(d(x1))) = 16x1 + 31 >= x1 + 11 = c#(x1)
    
    b#(d(d(x1))) = 16x1 + 31 >= 4x1 + 18 = d#(c(x1))
    
    b#(d(d(x1))) = 16x1 + 31 >= 16x1 + 30 = d#(d(c(x1)))
    
    b#(d(d(x1))) = 16x1 + 31 >= 16x1 + 27 = c#(d(d(c(x1))))
    
    b#(d(d(x1))) = 16x1 + 31 >= 16x1 + 28 = c#(c(d(d(c(x1)))))
    
    d(a(x1)) = 4x1 + 20 >= 4x1 + 19 = b(d(x1))
    
    b(x1) = x1 + 19 >= x1 + 15 = a(a(a(x1)))
    
    c(d(c(x1))) = 4x1 + 5 >= 4x1 + 5 = a(d(x1))
    
    b(d(d(x1))) = 16x1 + 19 >= 16x1 + 18 = c(c(d(d(c(x1)))))
   problem:
    DPs:
     
    TRS:
     d(a(x1)) -> b(d(x1))
     b(x1) -> a(a(a(x1)))
     c(d(c(x1))) -> a(d(x1))
     b(d(d(x1))) -> c(c(d(d(c(x1)))))
   Qed