YES

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

Proof:
 DP Processor:
  DPs:
   a#(b(a(x1))) -> c#(x1)
   a#(b(a(x1))) -> b#(c(x1))
   b#(b(b(x1))) -> c#(b(x1))
   c#(x1) -> b#(x1)
   c#(x1) -> a#(b(x1))
   c#(d(x1)) -> a#(x1)
   c#(d(x1)) -> b#(a(x1))
   c#(d(x1)) -> c#(b(a(x1)))
  TRS:
   a(b(a(x1))) -> b(c(x1))
   b(b(b(x1))) -> c(b(x1))
   c(x1) -> a(b(x1))
   c(d(x1)) -> d(c(b(a(x1))))
  TDG Processor:
   DPs:
    a#(b(a(x1))) -> c#(x1)
    a#(b(a(x1))) -> b#(c(x1))
    b#(b(b(x1))) -> c#(b(x1))
    c#(x1) -> b#(x1)
    c#(x1) -> a#(b(x1))
    c#(d(x1)) -> a#(x1)
    c#(d(x1)) -> b#(a(x1))
    c#(d(x1)) -> c#(b(a(x1)))
   TRS:
    a(b(a(x1))) -> b(c(x1))
    b(b(b(x1))) -> c(b(x1))
    c(x1) -> a(b(x1))
    c(d(x1)) -> d(c(b(a(x1))))
   graph:
    b#(b(b(x1))) -> c#(b(x1)) -> c#(d(x1)) -> c#(b(a(x1)))
    b#(b(b(x1))) -> c#(b(x1)) -> c#(d(x1)) -> b#(a(x1))
    b#(b(b(x1))) -> c#(b(x1)) -> c#(d(x1)) -> a#(x1)
    b#(b(b(x1))) -> c#(b(x1)) -> c#(x1) -> a#(b(x1))
    b#(b(b(x1))) -> c#(b(x1)) -> c#(x1) -> b#(x1)
    c#(d(x1)) -> b#(a(x1)) -> b#(b(b(x1))) -> c#(b(x1))
    c#(d(x1)) -> c#(b(a(x1))) -> c#(d(x1)) -> c#(b(a(x1)))
    c#(d(x1)) -> c#(b(a(x1))) -> c#(d(x1)) -> b#(a(x1))
    c#(d(x1)) -> c#(b(a(x1))) -> c#(d(x1)) -> a#(x1)
    c#(d(x1)) -> c#(b(a(x1))) -> c#(x1) -> a#(b(x1))
    c#(d(x1)) -> c#(b(a(x1))) -> c#(x1) -> b#(x1)
    c#(d(x1)) -> a#(x1) -> a#(b(a(x1))) -> b#(c(x1))
    c#(d(x1)) -> a#(x1) -> a#(b(a(x1))) -> c#(x1)
    c#(x1) -> b#(x1) -> b#(b(b(x1))) -> c#(b(x1))
    c#(x1) -> a#(b(x1)) -> a#(b(a(x1))) -> b#(c(x1))
    c#(x1) -> a#(b(x1)) -> a#(b(a(x1))) -> c#(x1)
    a#(b(a(x1))) -> b#(c(x1)) -> b#(b(b(x1))) -> c#(b(x1))
    a#(b(a(x1))) -> c#(x1) -> c#(d(x1)) -> c#(b(a(x1)))
    a#(b(a(x1))) -> c#(x1) -> c#(d(x1)) -> b#(a(x1))
    a#(b(a(x1))) -> c#(x1) -> c#(d(x1)) -> a#(x1)
    a#(b(a(x1))) -> c#(x1) -> c#(x1) -> a#(b(x1))
    a#(b(a(x1))) -> c#(x1) -> c#(x1) -> b#(x1)
   Arctic Interpretation Processor:
    dimension: 1
    interpretation:
     [b#](x0) = x0 + 0,
     
     [c#](x0) = x0 + 0,
     
     [a#](x0) = x0 + 0,
     
     [d](x0) = 1x0 + 5,
     
     [c](x0) = x0 + 0,
     
     [b](x0) = x0 + 0,
     
     [a](x0) = x0 + 0
    orientation:
     a#(b(a(x1))) = x1 + 0 >= x1 + 0 = c#(x1)
     
     a#(b(a(x1))) = x1 + 0 >= x1 + 0 = b#(c(x1))
     
     b#(b(b(x1))) = x1 + 0 >= x1 + 0 = c#(b(x1))
     
     c#(x1) = x1 + 0 >= x1 + 0 = b#(x1)
     
     c#(x1) = x1 + 0 >= x1 + 0 = a#(b(x1))
     
     c#(d(x1)) = 1x1 + 5 >= x1 + 0 = a#(x1)
     
     c#(d(x1)) = 1x1 + 5 >= x1 + 0 = b#(a(x1))
     
     c#(d(x1)) = 1x1 + 5 >= x1 + 0 = c#(b(a(x1)))
     
     a(b(a(x1))) = x1 + 0 >= x1 + 0 = b(c(x1))
     
     b(b(b(x1))) = x1 + 0 >= x1 + 0 = c(b(x1))
     
     c(x1) = x1 + 0 >= x1 + 0 = a(b(x1))
     
     c(d(x1)) = 1x1 + 5 >= 1x1 + 5 = d(c(b(a(x1))))
    problem:
     DPs:
      a#(b(a(x1))) -> c#(x1)
      a#(b(a(x1))) -> b#(c(x1))
      b#(b(b(x1))) -> c#(b(x1))
      c#(x1) -> b#(x1)
      c#(x1) -> a#(b(x1))
     TRS:
      a(b(a(x1))) -> b(c(x1))
      b(b(b(x1))) -> c(b(x1))
      c(x1) -> a(b(x1))
      c(d(x1)) -> d(c(b(a(x1))))
    EDG Processor:
     DPs:
      a#(b(a(x1))) -> c#(x1)
      a#(b(a(x1))) -> b#(c(x1))
      b#(b(b(x1))) -> c#(b(x1))
      c#(x1) -> b#(x1)
      c#(x1) -> a#(b(x1))
     TRS:
      a(b(a(x1))) -> b(c(x1))
      b(b(b(x1))) -> c(b(x1))
      c(x1) -> a(b(x1))
      c(d(x1)) -> d(c(b(a(x1))))
     graph:
      b#(b(b(x1))) -> c#(b(x1)) -> c#(x1) -> b#(x1)
      b#(b(b(x1))) -> c#(b(x1)) -> c#(x1) -> a#(b(x1))
      c#(x1) -> b#(x1) -> b#(b(b(x1))) -> c#(b(x1))
      c#(x1) -> a#(b(x1)) -> a#(b(a(x1))) -> c#(x1)
      c#(x1) -> a#(b(x1)) -> a#(b(a(x1))) -> b#(c(x1))
      a#(b(a(x1))) -> b#(c(x1)) -> b#(b(b(x1))) -> c#(b(x1))
      a#(b(a(x1))) -> c#(x1) -> c#(x1) -> b#(x1)
      a#(b(a(x1))) -> c#(x1) -> c#(x1) -> a#(b(x1))
     Arctic Interpretation Processor:
      dimension: 1
      interpretation:
       [b#](x0) = x0,
       
       [c#](x0) = 1x0,
       
       [a#](x0) = x0,
       
       [d](x0) = 14,
       
       [c](x0) = 2x0,
       
       [b](x0) = 1x0,
       
       [a](x0) = 1x0
      orientation:
       a#(b(a(x1))) = 2x1 >= 1x1 = c#(x1)
       
       a#(b(a(x1))) = 2x1 >= 2x1 = b#(c(x1))
       
       b#(b(b(x1))) = 2x1 >= 2x1 = c#(b(x1))
       
       c#(x1) = 1x1 >= x1 = b#(x1)
       
       c#(x1) = 1x1 >= 1x1 = a#(b(x1))
       
       a(b(a(x1))) = 3x1 >= 3x1 = b(c(x1))
       
       b(b(b(x1))) = 3x1 >= 3x1 = c(b(x1))
       
       c(x1) = 2x1 >= 2x1 = a(b(x1))
       
       c(d(x1)) = 16 >= 14 = d(c(b(a(x1))))
      problem:
       DPs:
        a#(b(a(x1))) -> b#(c(x1))
        b#(b(b(x1))) -> c#(b(x1))
        c#(x1) -> a#(b(x1))
       TRS:
        a(b(a(x1))) -> b(c(x1))
        b(b(b(x1))) -> c(b(x1))
        c(x1) -> a(b(x1))
        c(d(x1)) -> d(c(b(a(x1))))
      EDG Processor:
       DPs:
        a#(b(a(x1))) -> b#(c(x1))
        b#(b(b(x1))) -> c#(b(x1))
        c#(x1) -> a#(b(x1))
       TRS:
        a(b(a(x1))) -> b(c(x1))
        b(b(b(x1))) -> c(b(x1))
        c(x1) -> a(b(x1))
        c(d(x1)) -> d(c(b(a(x1))))
       graph:
        b#(b(b(x1))) -> c#(b(x1)) -> c#(x1) -> a#(b(x1))
        c#(x1) -> a#(b(x1)) -> a#(b(a(x1))) -> b#(c(x1))
        a#(b(a(x1))) -> b#(c(x1)) -> b#(b(b(x1))) -> c#(b(x1))
       Arctic Interpretation Processor:
        dimension: 3
        interpretation:
         [b#](x0) = [0  -& -&]x0 + [0],
         
         [c#](x0) = [0 0 0]x0 + [0],
         
         [a#](x0) = [-& 0  0 ]x0 + [0],
         
                   [0]
         [d](x0) = [0]
                   [1],
         
                   [0 0 1]     [0]
         [c](x0) = [0 0 1]x0 + [0]
                   [1 0 0]     [0],
         
                   [1  0  0 ]     [0 ]
         [b](x0) = [-& -& 0 ]x0 + [-&]
                   [0  -& -&]     [-&],
         
                   [-& 1  0 ]     [0]
         [a](x0) = [-& 1  0 ]x0 + [0]
                   [0  -& 1 ]     [0]
        orientation:
         a#(b(a(x1))) = [0 1 1]x1 + [0] >= [0 0 1]x1 + [0] = b#(c(x1))
         
         b#(b(b(x1))) = [2 1 1]x1 + [1] >= [1 0 0]x1 + [0] = c#(b(x1))
         
         c#(x1) = [0 0 0]x1 + [0] >= [0  -& 0 ]x1 + [0] = a#(b(x1))
         
                       [1 1 2]     [1]    [1 1 2]     [1]           
         a(b(a(x1))) = [1 1 2]x1 + [1] >= [1 0 0]x1 + [0] = b(c(x1))
                       [0 2 1]     [1]    [0 0 1]     [0]           
         
                       [3 2 2]     [2]    [1 0 0]     [0]           
         b(b(b(x1))) = [1 0 0]x1 + [0] >= [1 0 0]x1 + [0] = c(b(x1))
                       [2 1 1]     [1]    [2 1 1]     [1]           
         
                 [0 0 1]     [0]    [0  -& 1 ]     [0]           
         c(x1) = [0 0 1]x1 + [0] >= [0  -& 1 ]x1 + [0] = a(b(x1))
                 [1 0 0]     [0]    [1  0  0 ]     [0]           
         
                    [2]    [0]                 
         c(d(x1)) = [2] >= [0] = d(c(b(a(x1))))
                    [1]    [1]                 
        problem:
         DPs:
          a#(b(a(x1))) -> b#(c(x1))
          c#(x1) -> a#(b(x1))
         TRS:
          a(b(a(x1))) -> b(c(x1))
          b(b(b(x1))) -> c(b(x1))
          c(x1) -> a(b(x1))
          c(d(x1)) -> d(c(b(a(x1))))
        EDG Processor:
         DPs:
          a#(b(a(x1))) -> b#(c(x1))
          c#(x1) -> a#(b(x1))
         TRS:
          a(b(a(x1))) -> b(c(x1))
          b(b(b(x1))) -> c(b(x1))
          c(x1) -> a(b(x1))
          c(d(x1)) -> d(c(b(a(x1))))
         graph:
          c#(x1) -> a#(b(x1)) -> a#(b(a(x1))) -> b#(c(x1))
         SCC Processor:
          #sccs: 0
          #rules: 0
          #arcs: 1/4