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:
 DP Processor:
  DPs:
   a#(a(x1)) -> c#(x1)
   a#(a(x1)) -> d#(c(x1))
   a#(b(x1)) -> c#(x1)
   a#(b(x1)) -> c#(c(x1))
   a#(b(x1)) -> c#(c(c(x1)))
   b#(b(x1)) -> c#(x1)
   b#(b(x1)) -> c#(c(x1))
   b#(b(x1)) -> a#(c(c(x1)))
   c#(c(x1)) -> b#(x1)
   c#(d(x1)) -> a#(x1)
   c#(d(x1)) -> a#(a(x1))
   d#(d(x1)) -> c#(x1)
   d#(d(x1)) -> a#(c(x1))
   d#(d(x1)) -> b#(a(c(x1)))
  TRS:
   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)))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [b#](x0) = 16x0 + 11,
    
    [d#](x0) = 16x0 + 14,
    
    [c#](x0) = 16x0,
    
    [a#](x0) = 16x0 + 10,
    
    [b](x0) = x0 + 2,
    
    [d](x0) = x0 + 3,
    
    [c](x0) = x0 + 1,
    
    [a](x0) = x0 + 2
   orientation:
    a#(a(x1)) = 16x1 + 42 >= 16x1 = c#(x1)
    
    a#(a(x1)) = 16x1 + 42 >= 16x1 + 30 = d#(c(x1))
    
    a#(b(x1)) = 16x1 + 42 >= 16x1 = c#(x1)
    
    a#(b(x1)) = 16x1 + 42 >= 16x1 + 16 = c#(c(x1))
    
    a#(b(x1)) = 16x1 + 42 >= 16x1 + 32 = c#(c(c(x1)))
    
    b#(b(x1)) = 16x1 + 43 >= 16x1 = c#(x1)
    
    b#(b(x1)) = 16x1 + 43 >= 16x1 + 16 = c#(c(x1))
    
    b#(b(x1)) = 16x1 + 43 >= 16x1 + 42 = a#(c(c(x1)))
    
    c#(c(x1)) = 16x1 + 16 >= 16x1 + 11 = b#(x1)
    
    c#(d(x1)) = 16x1 + 48 >= 16x1 + 10 = a#(x1)
    
    c#(d(x1)) = 16x1 + 48 >= 16x1 + 42 = a#(a(x1))
    
    d#(d(x1)) = 16x1 + 62 >= 16x1 = c#(x1)
    
    d#(d(x1)) = 16x1 + 62 >= 16x1 + 26 = a#(c(x1))
    
    d#(d(x1)) = 16x1 + 62 >= 16x1 + 59 = b#(a(c(x1)))
    
    a(a(x1)) = x1 + 4 >= x1 + 4 = d(c(x1))
    
    a(b(x1)) = x1 + 4 >= x1 + 3 = c(c(c(x1)))
    
    b(b(x1)) = x1 + 4 >= x1 + 4 = a(c(c(x1)))
    
    c(c(x1)) = x1 + 2 >= x1 + 2 = b(x1)
    
    c(d(x1)) = x1 + 4 >= x1 + 4 = a(a(x1))
    
    d(d(x1)) = x1 + 6 >= x1 + 5 = b(a(c(x1)))
   problem:
    DPs:
     
    TRS:
     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)))
   Qed