YES

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

Proof:
 DP Processor:
  DPs:
   a#(d(x1)) -> b#(d(x1))
   a#(d(x1)) -> b#(c(b(d(x1))))
   a#(d(x1)) -> d#(b(c(b(d(x1)))))
   a#(x1) -> b#(x1)
   a#(x1) -> b#(b(x1))
   a#(x1) -> b#(f(b(b(x1))))
   a#(x1) -> b#(b(f(b(b(x1)))))
   b#(d(b(x1))) -> d#(x1)
   b#(d(b(x1))) -> a#(d(x1))
   d#(f(x1)) -> d#(x1)
   d#(f(x1)) -> b#(d(x1))
  TRS:
   a(d(x1)) -> d(b(c(b(d(x1)))))
   a(x1) -> b(b(f(b(b(x1)))))
   b(d(b(x1))) -> a(d(x1))
   d(f(x1)) -> b(d(x1))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [d#](x0) = 16x0,
    
    [b#](x0) = 2x0 + 1,
    
    [a#](x0) = 2x0 + 16,
    
    [f](x0) = x0 + 2,
    
    [c](x0) = 0,
    
    [b](x0) = x0 + 1,
    
    [a](x0) = x0 + 8,
    
    [d](x0) = 8x0 + 8
   orientation:
    a#(d(x1)) = 16x1 + 32 >= 16x1 + 17 = b#(d(x1))
    
    a#(d(x1)) = 16x1 + 32 >= 1 = b#(c(b(d(x1))))
    
    a#(d(x1)) = 16x1 + 32 >= 16 = d#(b(c(b(d(x1)))))
    
    a#(x1) = 2x1 + 16 >= 2x1 + 1 = b#(x1)
    
    a#(x1) = 2x1 + 16 >= 2x1 + 3 = b#(b(x1))
    
    a#(x1) = 2x1 + 16 >= 2x1 + 9 = b#(f(b(b(x1))))
    
    a#(x1) = 2x1 + 16 >= 2x1 + 11 = b#(b(f(b(b(x1)))))
    
    b#(d(b(x1))) = 16x1 + 33 >= 16x1 = d#(x1)
    
    b#(d(b(x1))) = 16x1 + 33 >= 16x1 + 32 = a#(d(x1))
    
    d#(f(x1)) = 16x1 + 32 >= 16x1 = d#(x1)
    
    d#(f(x1)) = 16x1 + 32 >= 16x1 + 17 = b#(d(x1))
    
    a(d(x1)) = 8x1 + 16 >= 16 = d(b(c(b(d(x1)))))
    
    a(x1) = x1 + 8 >= x1 + 6 = b(b(f(b(b(x1)))))
    
    b(d(b(x1))) = 8x1 + 17 >= 8x1 + 16 = a(d(x1))
    
    d(f(x1)) = 8x1 + 24 >= 8x1 + 9 = b(d(x1))
   problem:
    DPs:
     
    TRS:
     a(d(x1)) -> d(b(c(b(d(x1)))))
     a(x1) -> b(b(f(b(b(x1)))))
     b(d(b(x1))) -> a(d(x1))
     d(f(x1)) -> b(d(x1))
   Qed