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)))))
  TDG 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)))))
   graph:
    c#(d(c(x1))) -> d#(x1) -> d#(a(x1)) -> b#(d(x1))
    c#(d(c(x1))) -> d#(x1) -> d#(a(x1)) -> d#(x1)
    b#(d(d(x1))) -> c#(c(d(d(c(x1))))) -> c#(d(c(x1))) -> d#(x1)
    b#(d(d(x1))) -> c#(d(d(c(x1)))) -> c#(d(c(x1))) -> d#(x1)
    b#(d(d(x1))) -> c#(x1) -> c#(d(c(x1))) -> d#(x1)
    b#(d(d(x1))) -> d#(c(x1)) -> d#(a(x1)) -> b#(d(x1))
    b#(d(d(x1))) -> d#(c(x1)) -> d#(a(x1)) -> d#(x1)
    b#(d(d(x1))) -> d#(d(c(x1))) -> d#(a(x1)) -> b#(d(x1))
    b#(d(d(x1))) -> d#(d(c(x1))) -> d#(a(x1)) -> d#(x1)
    d#(a(x1)) -> b#(d(x1)) -> b#(d(d(x1))) -> c#(c(d(d(c(x1)))))
    d#(a(x1)) -> b#(d(x1)) -> b#(d(d(x1))) -> c#(d(d(c(x1))))
    d#(a(x1)) -> b#(d(x1)) -> b#(d(d(x1))) -> d#(d(c(x1)))
    d#(a(x1)) -> b#(d(x1)) -> b#(d(d(x1))) -> d#(c(x1))
    d#(a(x1)) -> b#(d(x1)) -> b#(d(d(x1))) -> c#(x1)
    d#(a(x1)) -> d#(x1) -> d#(a(x1)) -> b#(d(x1))
    d#(a(x1)) -> d#(x1) -> d#(a(x1)) -> d#(x1)
   EDG 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)))))
    graph:
     c#(d(c(x1))) -> d#(x1) -> d#(a(x1)) -> d#(x1)
     c#(d(c(x1))) -> d#(x1) -> d#(a(x1)) -> b#(d(x1))
     b#(d(d(x1))) -> c#(d(d(c(x1)))) -> c#(d(c(x1))) -> d#(x1)
     b#(d(d(x1))) -> c#(x1) -> c#(d(c(x1))) -> d#(x1)
     b#(d(d(x1))) -> d#(c(x1)) -> d#(a(x1)) -> d#(x1)
     b#(d(d(x1))) -> d#(c(x1)) -> d#(a(x1)) -> b#(d(x1))
     b#(d(d(x1))) -> d#(d(c(x1))) -> d#(a(x1)) -> d#(x1)
     b#(d(d(x1))) -> d#(d(c(x1))) -> d#(a(x1)) -> b#(d(x1))
     d#(a(x1)) -> b#(d(x1)) -> b#(d(d(x1))) -> c#(x1)
     d#(a(x1)) -> b#(d(x1)) -> b#(d(d(x1))) -> d#(c(x1))
     d#(a(x1)) -> b#(d(x1)) -> b#(d(d(x1))) -> d#(d(c(x1)))
     d#(a(x1)) -> b#(d(x1)) -> b#(d(d(x1))) -> c#(d(d(c(x1))))
     d#(a(x1)) -> b#(d(x1)) -> b#(d(d(x1))) -> c#(c(d(d(c(x1)))))
     d#(a(x1)) -> d#(x1) -> d#(a(x1)) -> d#(x1)
     d#(a(x1)) -> d#(x1) -> d#(a(x1)) -> b#(d(x1))
    SCC Processor:
     #sccs: 1
     #rules: 7
     #arcs: 15/64
     DPs:
      c#(d(c(x1))) -> d#(x1)
      d#(a(x1)) -> b#(d(x1))
      b#(d(d(x1))) -> c#(d(d(c(x1))))
      b#(d(d(x1))) -> d#(d(c(x1)))
      d#(a(x1)) -> d#(x1)
      b#(d(d(x1))) -> d#(c(x1))
      b#(d(d(x1))) -> 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 + 1,
       
       [b#](x0) = x0 + 19,
       
       [d#](x0) = 4x0 + 2,
       
       [c](x0) = x0 + 1,
       
       [b](x0) = x0 + 18,
       
       [d](x0) = 4x0,
       
       [a](x0) = x0 + 5
      orientation:
       c#(d(c(x1))) = 4x1 + 5 >= 4x1 + 2 = d#(x1)
       
       d#(a(x1)) = 4x1 + 22 >= 4x1 + 19 = b#(d(x1))
       
       b#(d(d(x1))) = 16x1 + 19 >= 16x1 + 17 = c#(d(d(c(x1))))
       
       b#(d(d(x1))) = 16x1 + 19 >= 16x1 + 18 = d#(d(c(x1)))
       
       d#(a(x1)) = 4x1 + 22 >= 4x1 + 2 = d#(x1)
       
       b#(d(d(x1))) = 16x1 + 19 >= 4x1 + 6 = d#(c(x1))
       
       b#(d(d(x1))) = 16x1 + 19 >= x1 + 1 = c#(x1)
       
       d(a(x1)) = 4x1 + 20 >= 4x1 + 18 = b(d(x1))
       
       b(x1) = x1 + 18 >= x1 + 15 = a(a(a(x1)))
       
       c(d(c(x1))) = 4x1 + 5 >= 4x1 + 5 = a(d(x1))
       
       b(d(d(x1))) = 16x1 + 18 >= 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