YES

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

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