YES

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

Proof:
 String Reversal Processor:
  a(a(x1)) -> c(b(x1))
  b(a(x1)) -> a(c(x1))
  c(c(x1)) -> b(a(x1))
  DP Processor:
   DPs:
    a#(a(x1)) -> b#(x1)
    a#(a(x1)) -> c#(b(x1))
    b#(a(x1)) -> c#(x1)
    b#(a(x1)) -> a#(c(x1))
    c#(c(x1)) -> a#(x1)
    c#(c(x1)) -> b#(a(x1))
   TRS:
    a(a(x1)) -> c(b(x1))
    b(a(x1)) -> a(c(x1))
    c(c(x1)) -> b(a(x1))
   TDG Processor:
    DPs:
     a#(a(x1)) -> b#(x1)
     a#(a(x1)) -> c#(b(x1))
     b#(a(x1)) -> c#(x1)
     b#(a(x1)) -> a#(c(x1))
     c#(c(x1)) -> a#(x1)
     c#(c(x1)) -> b#(a(x1))
    TRS:
     a(a(x1)) -> c(b(x1))
     b(a(x1)) -> a(c(x1))
     c(c(x1)) -> b(a(x1))
    graph:
     c#(c(x1)) -> b#(a(x1)) -> b#(a(x1)) -> a#(c(x1))
     c#(c(x1)) -> b#(a(x1)) -> b#(a(x1)) -> c#(x1)
     c#(c(x1)) -> a#(x1) -> a#(a(x1)) -> c#(b(x1))
     c#(c(x1)) -> a#(x1) -> a#(a(x1)) -> b#(x1)
     b#(a(x1)) -> c#(x1) -> c#(c(x1)) -> b#(a(x1))
     b#(a(x1)) -> c#(x1) -> c#(c(x1)) -> a#(x1)
     b#(a(x1)) -> a#(c(x1)) -> a#(a(x1)) -> c#(b(x1))
     b#(a(x1)) -> a#(c(x1)) -> a#(a(x1)) -> b#(x1)
     a#(a(x1)) -> c#(b(x1)) -> c#(c(x1)) -> b#(a(x1))
     a#(a(x1)) -> c#(b(x1)) -> c#(c(x1)) -> a#(x1)
     a#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(c(x1))
     a#(a(x1)) -> b#(x1) -> b#(a(x1)) -> c#(x1)
    Arctic Interpretation Processor:
     dimension: 1
     interpretation:
      [c#](x0) = -8x0 + 0,
      
      [b#](x0) = -8x0 + 4,
      
      [a#](x0) = -8x0 + 0,
      
      [b](x0) = 1x0 + -10,
      
      [c](x0) = 1x0 + 12,
      
      [a](x0) = 1x0 + 12
     orientation:
      a#(a(x1)) = -7x1 + 4 >= -8x1 + 4 = b#(x1)
      
      a#(a(x1)) = -7x1 + 4 >= -7x1 + 0 = c#(b(x1))
      
      b#(a(x1)) = -7x1 + 4 >= -8x1 + 0 = c#(x1)
      
      b#(a(x1)) = -7x1 + 4 >= -7x1 + 4 = a#(c(x1))
      
      c#(c(x1)) = -7x1 + 4 >= -8x1 + 0 = a#(x1)
      
      c#(c(x1)) = -7x1 + 4 >= -7x1 + 4 = b#(a(x1))
      
      a(a(x1)) = 2x1 + 13 >= 2x1 + 12 = c(b(x1))
      
      b(a(x1)) = 2x1 + 13 >= 2x1 + 13 = a(c(x1))
      
      c(c(x1)) = 2x1 + 13 >= 2x1 + 13 = b(a(x1))
     problem:
      DPs:
       a#(a(x1)) -> b#(x1)
       a#(a(x1)) -> c#(b(x1))
       b#(a(x1)) -> a#(c(x1))
       c#(c(x1)) -> b#(a(x1))
      TRS:
       a(a(x1)) -> c(b(x1))
       b(a(x1)) -> a(c(x1))
       c(c(x1)) -> b(a(x1))
     EDG Processor:
      DPs:
       a#(a(x1)) -> b#(x1)
       a#(a(x1)) -> c#(b(x1))
       b#(a(x1)) -> a#(c(x1))
       c#(c(x1)) -> b#(a(x1))
      TRS:
       a(a(x1)) -> c(b(x1))
       b(a(x1)) -> a(c(x1))
       c(c(x1)) -> b(a(x1))
      graph:
       c#(c(x1)) -> b#(a(x1)) -> b#(a(x1)) -> a#(c(x1))
       b#(a(x1)) -> a#(c(x1)) -> a#(a(x1)) -> b#(x1)
       b#(a(x1)) -> a#(c(x1)) -> a#(a(x1)) -> c#(b(x1))
       a#(a(x1)) -> c#(b(x1)) -> c#(c(x1)) -> b#(a(x1))
       a#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(c(x1))
      Arctic Interpretation Processor:
       dimension: 2
       interpretation:
        [c#](x0) = [2  -&]x0,
        
        [b#](x0) = [2  -&]x0,
        
        [a#](x0) = [2  -&]x0,
        
                  [1  -&]     [-&]
        [b](x0) = [0  3 ]x0 + [1 ],
        
                  [1  -&]     [-&]
        [c](x0) = [0  3 ]x0 + [1 ],
        
                  [1  -&]     [-&]
        [a](x0) = [0  3 ]x0 + [1 ]
       orientation:
        a#(a(x1)) = [3  -&]x1 >= [2  -&]x1 = b#(x1)
        
        a#(a(x1)) = [3  -&]x1 >= [3  -&]x1 = c#(b(x1))
        
        b#(a(x1)) = [3  -&]x1 >= [3  -&]x1 = a#(c(x1))
        
        c#(c(x1)) = [3  -&]x1 >= [3  -&]x1 = b#(a(x1))
        
                   [2  -&]     [-&]    [2  -&]     [-&]           
        a(a(x1)) = [3  6 ]x1 + [4 ] >= [3  6 ]x1 + [4 ] = c(b(x1))
        
                   [2  -&]     [-&]    [2  -&]     [-&]           
        b(a(x1)) = [3  6 ]x1 + [4 ] >= [3  6 ]x1 + [4 ] = a(c(x1))
        
                   [2  -&]     [-&]    [2  -&]     [-&]           
        c(c(x1)) = [3  6 ]x1 + [4 ] >= [3  6 ]x1 + [4 ] = b(a(x1))
       problem:
        DPs:
         a#(a(x1)) -> c#(b(x1))
         b#(a(x1)) -> a#(c(x1))
         c#(c(x1)) -> b#(a(x1))
        TRS:
         a(a(x1)) -> c(b(x1))
         b(a(x1)) -> a(c(x1))
         c(c(x1)) -> b(a(x1))
       EDG Processor:
        DPs:
         a#(a(x1)) -> c#(b(x1))
         b#(a(x1)) -> a#(c(x1))
         c#(c(x1)) -> b#(a(x1))
        TRS:
         a(a(x1)) -> c(b(x1))
         b(a(x1)) -> a(c(x1))
         c(c(x1)) -> b(a(x1))
        graph:
         c#(c(x1)) -> b#(a(x1)) -> b#(a(x1)) -> a#(c(x1))
         b#(a(x1)) -> a#(c(x1)) -> a#(a(x1)) -> c#(b(x1))
         a#(a(x1)) -> c#(b(x1)) -> c#(c(x1)) -> b#(a(x1))
        Arctic Interpretation Processor:
         dimension: 3
         interpretation:
          [c#](x0) = [0 0 0]x0 + [0],
          
          [b#](x0) = [1  -& 0 ]x0 + [1],
          
          [a#](x0) = [0  0  -&]x0 + [0],
          
                    [1  -& 0 ]     [0]
          [b](x0) = [1  -& 0 ]x0 + [1]
                    [0  -& -&]     [0],
          
                    [-& -& 0 ]     [0]
          [c](x0) = [-& -& 0 ]x0 + [0]
                    [0  0  1 ]     [1],
          
                    [-& -& 0 ]     [0]
          [a](x0) = [1  0  0 ]x0 + [1]
                    [0  0  -&]     [0]
         orientation:
          a#(a(x1)) = [1 0 0]x1 + [1] >= [1  -& 0 ]x1 + [1] = c#(b(x1))
          
          b#(a(x1)) = [0 0 1]x1 + [1] >= [-& -& 0 ]x1 + [0] = a#(c(x1))
          
          c#(c(x1)) = [0 0 1]x1 + [1] >= [0 0 1]x1 + [1] = b#(a(x1))
          
                     [0  0  -&]     [0]    [0  -& -&]     [0]           
          a(a(x1)) = [1  0  1 ]x1 + [1] >= [0  -& -&]x1 + [0] = c(b(x1))
                     [1  0  0 ]     [1]    [1  -& 0 ]     [1]           
          
                     [0  0  1 ]     [1]    [0  0  1 ]     [1]           
          b(a(x1)) = [0  0  1 ]x1 + [1] >= [0  0  1 ]x1 + [1] = a(c(x1))
                     [-& -& 0 ]     [0]    [-& -& 0 ]     [0]           
          
                     [0 0 1]     [1]    [0  0  1 ]     [1]           
          c(c(x1)) = [0 0 1]x1 + [1] >= [0  0  1 ]x1 + [1] = b(a(x1))
                     [1 1 2]     [2]    [-& -& 0 ]     [0]           
         problem:
          DPs:
           a#(a(x1)) -> c#(b(x1))
           c#(c(x1)) -> b#(a(x1))
          TRS:
           a(a(x1)) -> c(b(x1))
           b(a(x1)) -> a(c(x1))
           c(c(x1)) -> b(a(x1))
         EDG Processor:
          DPs:
           a#(a(x1)) -> c#(b(x1))
           c#(c(x1)) -> b#(a(x1))
          TRS:
           a(a(x1)) -> c(b(x1))
           b(a(x1)) -> a(c(x1))
           c(c(x1)) -> b(a(x1))
          graph:
           a#(a(x1)) -> c#(b(x1)) -> c#(c(x1)) -> b#(a(x1))
          SCC Processor:
           #sccs: 0
           #rules: 0
           #arcs: 1/4