YES

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

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [c](x0) = x0 + 2,
   
   [b](x0) = x0 + 1,
   
   [a](x0) = x0,
   
   [d](x0) = x0 + 3
  orientation:
   c(c(c(a(x1)))) = x1 + 6 >= x1 + 6 = d(d(x1))
   
   d(b(x1)) = x1 + 4 >= x1 + 4 = c(c(x1))
   
   b(c(x1)) = x1 + 3 >= x1 + 3 = b(a(c(x1)))
   
   c(x1) = x1 + 2 >= x1 = a(a(x1))
   
   d(x1) = x1 + 3 >= x1 + 3 = b(c(x1))
  problem:
   c(c(c(a(x1)))) -> d(d(x1))
   d(b(x1)) -> c(c(x1))
   b(c(x1)) -> b(a(c(x1)))
   d(x1) -> b(c(x1))
  String Reversal Processor:
   a(c(c(c(x1)))) -> d(d(x1))
   b(d(x1)) -> c(c(x1))
   c(b(x1)) -> c(a(b(x1)))
   d(x1) -> c(b(x1))
   DP Processor:
    DPs:
     a#(c(c(c(x1)))) -> d#(x1)
     a#(c(c(c(x1)))) -> d#(d(x1))
     b#(d(x1)) -> c#(x1)
     b#(d(x1)) -> c#(c(x1))
     c#(b(x1)) -> a#(b(x1))
     c#(b(x1)) -> c#(a(b(x1)))
     d#(x1) -> b#(x1)
     d#(x1) -> c#(b(x1))
    TRS:
     a(c(c(c(x1)))) -> d(d(x1))
     b(d(x1)) -> c(c(x1))
     c(b(x1)) -> c(a(b(x1)))
     d(x1) -> c(b(x1))
    TDG Processor:
     DPs:
      a#(c(c(c(x1)))) -> d#(x1)
      a#(c(c(c(x1)))) -> d#(d(x1))
      b#(d(x1)) -> c#(x1)
      b#(d(x1)) -> c#(c(x1))
      c#(b(x1)) -> a#(b(x1))
      c#(b(x1)) -> c#(a(b(x1)))
      d#(x1) -> b#(x1)
      d#(x1) -> c#(b(x1))
     TRS:
      a(c(c(c(x1)))) -> d(d(x1))
      b(d(x1)) -> c(c(x1))
      c(b(x1)) -> c(a(b(x1)))
      d(x1) -> c(b(x1))
     graph:
      c#(b(x1)) -> c#(a(b(x1))) -> c#(b(x1)) -> c#(a(b(x1)))
      c#(b(x1)) -> c#(a(b(x1))) -> c#(b(x1)) -> a#(b(x1))
      c#(b(x1)) -> a#(b(x1)) -> a#(c(c(c(x1)))) -> d#(d(x1))
      c#(b(x1)) -> a#(b(x1)) -> a#(c(c(c(x1)))) -> d#(x1)
      b#(d(x1)) -> c#(c(x1)) -> c#(b(x1)) -> c#(a(b(x1)))
      b#(d(x1)) -> c#(c(x1)) -> c#(b(x1)) -> a#(b(x1))
      b#(d(x1)) -> c#(x1) -> c#(b(x1)) -> c#(a(b(x1)))
      b#(d(x1)) -> c#(x1) -> c#(b(x1)) -> a#(b(x1))
      d#(x1) -> c#(b(x1)) -> c#(b(x1)) -> c#(a(b(x1)))
      d#(x1) -> c#(b(x1)) -> c#(b(x1)) -> a#(b(x1))
      d#(x1) -> b#(x1) -> b#(d(x1)) -> c#(c(x1))
      d#(x1) -> b#(x1) -> b#(d(x1)) -> c#(x1)
      a#(c(c(c(x1)))) -> d#(d(x1)) -> d#(x1) -> c#(b(x1))
      a#(c(c(c(x1)))) -> d#(d(x1)) -> d#(x1) -> b#(x1)
      a#(c(c(c(x1)))) -> d#(x1) -> d#(x1) -> c#(b(x1))
      a#(c(c(c(x1)))) -> d#(x1) -> d#(x1) -> b#(x1)
     EDG Processor:
      DPs:
       a#(c(c(c(x1)))) -> d#(x1)
       a#(c(c(c(x1)))) -> d#(d(x1))
       b#(d(x1)) -> c#(x1)
       b#(d(x1)) -> c#(c(x1))
       c#(b(x1)) -> a#(b(x1))
       c#(b(x1)) -> c#(a(b(x1)))
       d#(x1) -> b#(x1)
       d#(x1) -> c#(b(x1))
      TRS:
       a(c(c(c(x1)))) -> d(d(x1))
       b(d(x1)) -> c(c(x1))
       c(b(x1)) -> c(a(b(x1)))
       d(x1) -> c(b(x1))
      graph:
       c#(b(x1)) -> a#(b(x1)) -> a#(c(c(c(x1)))) -> d#(x1)
       c#(b(x1)) -> a#(b(x1)) -> a#(c(c(c(x1)))) -> d#(d(x1))
       b#(d(x1)) -> c#(x1) -> c#(b(x1)) -> a#(b(x1))
       b#(d(x1)) -> c#(x1) -> c#(b(x1)) -> c#(a(b(x1)))
       d#(x1) -> c#(b(x1)) -> c#(b(x1)) -> a#(b(x1))
       d#(x1) -> c#(b(x1)) -> c#(b(x1)) -> c#(a(b(x1)))
       d#(x1) -> b#(x1) -> b#(d(x1)) -> c#(x1)
       d#(x1) -> b#(x1) -> b#(d(x1)) -> c#(c(x1))
       a#(c(c(c(x1)))) -> d#(d(x1)) -> d#(x1) -> b#(x1)
       a#(c(c(c(x1)))) -> d#(d(x1)) -> d#(x1) -> c#(b(x1))
       a#(c(c(c(x1)))) -> d#(x1) -> d#(x1) -> b#(x1)
       a#(c(c(c(x1)))) -> d#(x1) -> d#(x1) -> c#(b(x1))
      SCC Processor:
       #sccs: 1
       #rules: 6
       #arcs: 12/64
       DPs:
        c#(b(x1)) -> a#(b(x1))
        a#(c(c(c(x1)))) -> d#(d(x1))
        d#(x1) -> c#(b(x1))
        d#(x1) -> b#(x1)
        b#(d(x1)) -> c#(x1)
        a#(c(c(c(x1)))) -> d#(x1)
       TRS:
        a(c(c(c(x1)))) -> d(d(x1))
        b(d(x1)) -> c(c(x1))
        c(b(x1)) -> c(a(b(x1)))
        d(x1) -> c(b(x1))
       Arctic Interpretation Processor:
        dimension: 1
        usable rules:
         a(c(c(c(x1)))) -> d(d(x1))
         b(d(x1)) -> c(c(x1))
         c(b(x1)) -> c(a(b(x1)))
         d(x1) -> c(b(x1))
        interpretation:
         [a#](x0) = x0 + 0,
         
         [c](x0) = 8x0 + 5,
         
         [b](x0) = 4x0 + 0,
         
         [d#](x0) = 8x0 + 0,
         
         [a](x0) = x0 + 0,
         
         [c#](x0) = x0 + 0,
         
         [b#](x0) = 6x0,
         
         [d](x0) = 12x0 + 9
        orientation:
         c#(b(x1)) = 4x1 + 0 >= 4x1 + 0 = a#(b(x1))
         
         a#(c(c(c(x1)))) = 24x1 + 21 >= 20x1 + 17 = d#(d(x1))
         
         d#(x1) = 8x1 + 0 >= 4x1 + 0 = c#(b(x1))
         
         d#(x1) = 8x1 + 0 >= 6x1 = b#(x1)
         
         b#(d(x1)) = 18x1 + 15 >= x1 + 0 = c#(x1)
         
         a#(c(c(c(x1)))) = 24x1 + 21 >= 8x1 + 0 = d#(x1)
         
         a(c(c(c(x1)))) = 24x1 + 21 >= 24x1 + 21 = d(d(x1))
         
         b(d(x1)) = 16x1 + 13 >= 16x1 + 13 = c(c(x1))
         
         c(b(x1)) = 12x1 + 8 >= 12x1 + 8 = c(a(b(x1)))
         
         d(x1) = 12x1 + 9 >= 12x1 + 8 = c(b(x1))
        problem:
         DPs:
          c#(b(x1)) -> a#(b(x1))
          d#(x1) -> c#(b(x1))
         TRS:
          a(c(c(c(x1)))) -> d(d(x1))
          b(d(x1)) -> c(c(x1))
          c(b(x1)) -> c(a(b(x1)))
          d(x1) -> c(b(x1))
        Restore Modifier:
         DPs:
          c#(b(x1)) -> a#(b(x1))
          d#(x1) -> c#(b(x1))
         TRS:
          a(c(c(c(x1)))) -> d(d(x1))
          b(d(x1)) -> c(c(x1))
          c(b(x1)) -> c(a(b(x1)))
          d(x1) -> c(b(x1))
         EDG Processor:
          DPs:
           c#(b(x1)) -> a#(b(x1))
           d#(x1) -> c#(b(x1))
          TRS:
           a(c(c(c(x1)))) -> d(d(x1))
           b(d(x1)) -> c(c(x1))
           c(b(x1)) -> c(a(b(x1)))
           d(x1) -> c(b(x1))
          graph:
           d#(x1) -> c#(b(x1)) -> c#(b(x1)) -> a#(b(x1))
          SCC Processor:
           #sccs: 0
           #rules: 0
           #arcs: 1/4