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:
 Arctic Interpretation Processor:
  dimension: 2
  interpretation:
             [0 2]  
   [d](x0) = [2 3]x0,
   
             [0  0 ]  
   [c](x0) = [-& 1 ]x0,
   
             [0  0 ]  
   [b](x0) = [-& -&]x0,
   
             [0  1 ]  
   [a](x0) = [-& 0 ]x0
  orientation:
                 [0  1 ]      [0  1 ]             
   a(b(a(x1))) = [-& -&]x1 >= [-& -&]x1 = b(c(x1))
   
                 [0  0 ]      [0  0 ]             
   b(b(b(x1))) = [-& -&]x1 >= [-& -&]x1 = c(b(x1))
   
           [0  0 ]      [0  0 ]             
   c(x1) = [-& 1 ]x1 >= [-& -&]x1 = a(b(x1))
   
              [2 3]      [0 1]                   
   c(d(x1)) = [3 4]x1 >= [2 3]x1 = d(c(b(a(x1))))
  problem:
   a(b(a(x1))) -> b(c(x1))
   b(b(b(x1))) -> c(b(x1))
   c(x1) -> a(b(x1))
  String Reversal Processor:
   a(b(a(x1))) -> c(b(x1))
   b(b(b(x1))) -> b(c(x1))
   c(x1) -> b(a(x1))
   DP Processor:
    DPs:
     a#(b(a(x1))) -> b#(x1)
     a#(b(a(x1))) -> c#(b(x1))
     b#(b(b(x1))) -> c#(x1)
     b#(b(b(x1))) -> b#(c(x1))
     c#(x1) -> a#(x1)
     c#(x1) -> b#(a(x1))
    TRS:
     a(b(a(x1))) -> c(b(x1))
     b(b(b(x1))) -> b(c(x1))
     c(x1) -> b(a(x1))
    TDG Processor:
     DPs:
      a#(b(a(x1))) -> b#(x1)
      a#(b(a(x1))) -> c#(b(x1))
      b#(b(b(x1))) -> c#(x1)
      b#(b(b(x1))) -> b#(c(x1))
      c#(x1) -> a#(x1)
      c#(x1) -> b#(a(x1))
     TRS:
      a(b(a(x1))) -> c(b(x1))
      b(b(b(x1))) -> b(c(x1))
      c(x1) -> b(a(x1))
     graph:
      c#(x1) -> b#(a(x1)) -> b#(b(b(x1))) -> b#(c(x1))
      c#(x1) -> b#(a(x1)) -> b#(b(b(x1))) -> c#(x1)
      c#(x1) -> a#(x1) -> a#(b(a(x1))) -> c#(b(x1))
      c#(x1) -> a#(x1) -> a#(b(a(x1))) -> b#(x1)
      b#(b(b(x1))) -> c#(x1) -> c#(x1) -> b#(a(x1))
      b#(b(b(x1))) -> c#(x1) -> c#(x1) -> a#(x1)
      b#(b(b(x1))) -> b#(c(x1)) -> b#(b(b(x1))) -> b#(c(x1))
      b#(b(b(x1))) -> b#(c(x1)) -> b#(b(b(x1))) -> c#(x1)
      a#(b(a(x1))) -> c#(b(x1)) -> c#(x1) -> b#(a(x1))
      a#(b(a(x1))) -> c#(b(x1)) -> c#(x1) -> a#(x1)
      a#(b(a(x1))) -> b#(x1) -> b#(b(b(x1))) -> b#(c(x1))
      a#(b(a(x1))) -> b#(x1) -> b#(b(b(x1))) -> c#(x1)
     Arctic Interpretation Processor:
      dimension: 2
      usable rules:
       a(b(a(x1))) -> c(b(x1))
       b(b(b(x1))) -> b(c(x1))
       c(x1) -> b(a(x1))
      interpretation:
       [c#](x0) = [1 1]x0 + [0],
       
       [b#](x0) = [0 0]x0 + [0],
       
       [a#](x0) = [0 0]x0,
       
                 [0  -&]     [0]
       [c](x0) = [2  2 ]x0 + [1],
       
                 [0  -&]     [0]
       [b](x0) = [1  1 ]x0 + [0],
       
                 [0  -&]     [0]
       [a](x0) = [1  1 ]x0 + [0]
      orientation:
       a#(b(a(x1))) = [2 2]x1 + [1] >= [0 0]x1 + [0] = b#(x1)
       
       a#(b(a(x1))) = [2 2]x1 + [1] >= [2 2]x1 + [1] = c#(b(x1))
       
       b#(b(b(x1))) = [2 2]x1 + [1] >= [1 1]x1 + [0] = c#(x1)
       
       b#(b(b(x1))) = [2 2]x1 + [1] >= [2 2]x1 + [1] = b#(c(x1))
       
       c#(x1) = [1 1]x1 + [0] >= [0 0]x1 = a#(x1)
       
       c#(x1) = [1 1]x1 + [0] >= [1 1]x1 + [0] = b#(a(x1))
       
                     [0  -&]     [0]    [0  -&]     [0]           
       a(b(a(x1))) = [3  3 ]x1 + [2] >= [3  3 ]x1 + [2] = c(b(x1))
       
                     [0  -&]     [0]    [0  -&]     [0]           
       b(b(b(x1))) = [3  3 ]x1 + [2] >= [3  3 ]x1 + [2] = b(c(x1))
       
               [0  -&]     [0]    [0  -&]     [0]           
       c(x1) = [2  2 ]x1 + [1] >= [2  2 ]x1 + [1] = b(a(x1))
      problem:
       DPs:
        a#(b(a(x1))) -> c#(b(x1))
        b#(b(b(x1))) -> b#(c(x1))
        c#(x1) -> b#(a(x1))
       TRS:
        a(b(a(x1))) -> c(b(x1))
        b(b(b(x1))) -> b(c(x1))
        c(x1) -> b(a(x1))
      Restore Modifier:
       DPs:
        a#(b(a(x1))) -> c#(b(x1))
        b#(b(b(x1))) -> b#(c(x1))
        c#(x1) -> b#(a(x1))
       TRS:
        a(b(a(x1))) -> c(b(x1))
        b(b(b(x1))) -> b(c(x1))
        c(x1) -> b(a(x1))
       EDG Processor:
        DPs:
         a#(b(a(x1))) -> c#(b(x1))
         b#(b(b(x1))) -> b#(c(x1))
         c#(x1) -> b#(a(x1))
        TRS:
         a(b(a(x1))) -> c(b(x1))
         b(b(b(x1))) -> b(c(x1))
         c(x1) -> b(a(x1))
        graph:
         c#(x1) -> b#(a(x1)) -> b#(b(b(x1))) -> b#(c(x1))
         b#(b(b(x1))) -> b#(c(x1)) -> b#(b(b(x1))) -> b#(c(x1))
         a#(b(a(x1))) -> c#(b(x1)) -> c#(x1) -> b#(a(x1))
        SCC Processor:
         #sccs: 1
         #rules: 1
         #arcs: 3/9
         DPs:
          b#(b(b(x1))) -> b#(c(x1))
         TRS:
          a(b(a(x1))) -> c(b(x1))
          b(b(b(x1))) -> b(c(x1))
          c(x1) -> b(a(x1))
         Arctic Interpretation Processor:
          dimension: 3
          usable rules:
           a(b(a(x1))) -> c(b(x1))
           b(b(b(x1))) -> b(c(x1))
           c(x1) -> b(a(x1))
          interpretation:
           [b#](x0) = [-& 0  0 ]x0 + [0],
           
                     [0  1  -&]     [1]
           [c](x0) = [-& -& -&]x0 + [0]
                     [1  0  -&]     [1],
           
                     [-& 0  -&]     [0]
           [b](x0) = [-& -& -&]x0 + [0]
                     [1  -& 1 ]     [1],
           
                     [0  -& -&]     [0]
           [a](x0) = [0  1  -&]x0 + [1]
                     [0  -& -&]     [0]
          orientation:
           b#(b(b(x1))) = [2 1 2]x1 + [2] >= [1  0  -&]x1 + [1] = b#(c(x1))
           
                         [0  1  -&]     [1]    [-& 0  -&]     [1]           
           a(b(a(x1))) = [0  1  -&]x1 + [1] >= [-& -& -&]x1 + [0] = c(b(x1))
                         [0  1  -&]     [1]    [-& 1  -&]     [1]           
           
                         [-& -& -&]     [0]    [-& -& -&]     [0]           
           b(b(b(x1))) = [-& -& -&]x1 + [0] >= [-& -& -&]x1 + [0] = b(c(x1))
                         [3  2  3 ]     [3]    [2  2  -&]     [2]           
           
                   [0  1  -&]     [1]    [0  1  -&]     [1]           
           c(x1) = [-& -& -&]x1 + [0] >= [-& -& -&]x1 + [0] = b(a(x1))
                   [1  0  -&]     [1]    [1  -& -&]     [1]           
          problem:
           DPs:
            
           TRS:
            a(b(a(x1))) -> c(b(x1))
            b(b(b(x1))) -> b(c(x1))
            c(x1) -> b(a(x1))
          Qed