YES

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

Proof:
 DP Processor:
  DPs:
   b#(c(a(x1))) -> b#(x1)
   b#(b(b(x1))) -> c#(x1)
   b#(b(b(x1))) -> c#(a(c(x1)))
   c#(d(x1)) -> c#(x1)
   c#(d(x1)) -> d#(c(x1))
   c#(d(b(x1))) -> c#(x1)
   c#(d(b(x1))) -> c#(c(x1))
   c#(d(b(x1))) -> d#(c(c(x1)))
   d#(c(x1)) -> b#(x1)
   d#(c(x1)) -> b#(b(x1))
   d#(c(x1)) -> b#(b(b(x1)))
   c#(b(x1)) -> d#(a(x1))
   d#(a(x1)) -> b#(x1)
  TRS:
   b(c(a(x1))) -> a(b(x1))
   b(b(b(x1))) -> c(a(c(x1)))
   c(d(x1)) -> d(c(x1))
   c(d(b(x1))) -> d(c(c(x1)))
   d(c(x1)) -> b(b(b(x1)))
   c(b(x1)) -> d(a(x1))
   d(b(c(x1))) -> a(a(x1))
   d(a(x1)) -> b(x1)
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [d#](x0) = 8x0 + 17,
    
    [c#](x0) = 8x0 + 2,
    
    [b#](x0) = 8x0,
    
    [d](x0) = x0 + 4,
    
    [b](x0) = x0 + 2,
    
    [c](x0) = x0 + 2,
    
    [a](x0) = x0
   orientation:
    b#(c(a(x1))) = 8x1 + 16 >= 8x1 = b#(x1)
    
    b#(b(b(x1))) = 8x1 + 32 >= 8x1 + 2 = c#(x1)
    
    b#(b(b(x1))) = 8x1 + 32 >= 8x1 + 18 = c#(a(c(x1)))
    
    c#(d(x1)) = 8x1 + 34 >= 8x1 + 2 = c#(x1)
    
    c#(d(x1)) = 8x1 + 34 >= 8x1 + 33 = d#(c(x1))
    
    c#(d(b(x1))) = 8x1 + 50 >= 8x1 + 2 = c#(x1)
    
    c#(d(b(x1))) = 8x1 + 50 >= 8x1 + 18 = c#(c(x1))
    
    c#(d(b(x1))) = 8x1 + 50 >= 8x1 + 49 = d#(c(c(x1)))
    
    d#(c(x1)) = 8x1 + 33 >= 8x1 = b#(x1)
    
    d#(c(x1)) = 8x1 + 33 >= 8x1 + 16 = b#(b(x1))
    
    d#(c(x1)) = 8x1 + 33 >= 8x1 + 32 = b#(b(b(x1)))
    
    c#(b(x1)) = 8x1 + 18 >= 8x1 + 17 = d#(a(x1))
    
    d#(a(x1)) = 8x1 + 17 >= 8x1 = b#(x1)
    
    b(c(a(x1))) = x1 + 4 >= x1 + 2 = a(b(x1))
    
    b(b(b(x1))) = x1 + 6 >= x1 + 4 = c(a(c(x1)))
    
    c(d(x1)) = x1 + 6 >= x1 + 6 = d(c(x1))
    
    c(d(b(x1))) = x1 + 8 >= x1 + 8 = d(c(c(x1)))
    
    d(c(x1)) = x1 + 6 >= x1 + 6 = b(b(b(x1)))
    
    c(b(x1)) = x1 + 4 >= x1 + 4 = d(a(x1))
    
    d(b(c(x1))) = x1 + 8 >= x1 = a(a(x1))
    
    d(a(x1)) = x1 + 4 >= x1 + 2 = b(x1)
   problem:
    DPs:
     
    TRS:
     b(c(a(x1))) -> a(b(x1))
     b(b(b(x1))) -> c(a(c(x1)))
     c(d(x1)) -> d(c(x1))
     c(d(b(x1))) -> d(c(c(x1)))
     d(c(x1)) -> b(b(b(x1)))
     c(b(x1)) -> d(a(x1))
     d(b(c(x1))) -> a(a(x1))
     d(a(x1)) -> b(x1)
   Qed