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:
 Arctic Interpretation Processor:
  dimension: 1
  interpretation:
   [b](x0) = 3x0,
   
   [d](x0) = 9x0,
   
   [c](x0) = 6x0,
   
   [a](x0) = x0
  orientation:
   c(c(c(a(x1)))) = 18x1 >= 18x1 = d(d(x1))
   
   d(b(x1)) = 12x1 >= 12x1 = c(c(x1))
   
   b(c(x1)) = 9x1 >= 9x1 = b(a(c(x1)))
   
   c(x1) = 6x1 >= x1 = a(a(x1))
   
   d(x1) = 9x1 >= 9x1 = 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
        interpretation:
         [c#](x0) = 1x0,
         
         [b#](x0) = 1x0,
         
         [d#](x0) = 3x0,
         
         [a#](x0) = 1x0,
         
         [b](x0) = 2x0,
         
         [d](x0) = 6x0,
         
         [c](x0) = 4x0,
         
         [a](x0) = x0
        orientation:
         c#(b(x1)) = 3x1 >= 3x1 = a#(b(x1))
         
         a#(c(c(c(x1)))) = 13x1 >= 9x1 = d#(d(x1))
         
         d#(x1) = 3x1 >= 3x1 = c#(b(x1))
         
         d#(x1) = 3x1 >= 1x1 = b#(x1)
         
         b#(d(x1)) = 7x1 >= 1x1 = c#(x1)
         
         a#(c(c(c(x1)))) = 13x1 >= 3x1 = d#(x1)
         
         a(c(c(c(x1)))) = 12x1 >= 12x1 = d(d(x1))
         
         b(d(x1)) = 8x1 >= 8x1 = c(c(x1))
         
         c(b(x1)) = 6x1 >= 6x1 = c(a(b(x1)))
         
         d(x1) = 6x1 >= 6x1 = 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))
        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