YES

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

Proof:
 String Reversal Processor:
  a(a(x1)) -> b(c(x1))
  b(b(x1)) -> a(c(x1))
  c(c(x1)) -> a(b(x1))
  DP Processor:
   DPs:
    a#(a(x1)) -> c#(x1)
    a#(a(x1)) -> b#(c(x1))
    b#(b(x1)) -> c#(x1)
    b#(b(x1)) -> a#(c(x1))
    c#(c(x1)) -> b#(x1)
    c#(c(x1)) -> a#(b(x1))
   TRS:
    a(a(x1)) -> b(c(x1))
    b(b(x1)) -> a(c(x1))
    c(c(x1)) -> a(b(x1))
   TDG Processor:
    DPs:
     a#(a(x1)) -> c#(x1)
     a#(a(x1)) -> b#(c(x1))
     b#(b(x1)) -> c#(x1)
     b#(b(x1)) -> a#(c(x1))
     c#(c(x1)) -> b#(x1)
     c#(c(x1)) -> a#(b(x1))
    TRS:
     a(a(x1)) -> b(c(x1))
     b(b(x1)) -> a(c(x1))
     c(c(x1)) -> a(b(x1))
    graph:
     b#(b(x1)) -> c#(x1) -> c#(c(x1)) -> a#(b(x1))
     b#(b(x1)) -> c#(x1) -> c#(c(x1)) -> b#(x1)
     b#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> b#(c(x1))
     b#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> c#(x1)
     c#(c(x1)) -> b#(x1) -> b#(b(x1)) -> a#(c(x1))
     c#(c(x1)) -> b#(x1) -> b#(b(x1)) -> c#(x1)
     c#(c(x1)) -> a#(b(x1)) -> a#(a(x1)) -> b#(c(x1))
     c#(c(x1)) -> a#(b(x1)) -> a#(a(x1)) -> c#(x1)
     a#(a(x1)) -> b#(c(x1)) -> b#(b(x1)) -> a#(c(x1))
     a#(a(x1)) -> b#(c(x1)) -> b#(b(x1)) -> c#(x1)
     a#(a(x1)) -> c#(x1) -> c#(c(x1)) -> a#(b(x1))
     a#(a(x1)) -> c#(x1) -> c#(c(x1)) -> b#(x1)
    Arctic Interpretation Processor:
     dimension: 1
     usable rules:
      a(a(x1)) -> b(c(x1))
      b(b(x1)) -> a(c(x1))
      c(c(x1)) -> a(b(x1))
     interpretation:
      [c#](x0) = x0 + 0,
      
      [b](x0) = 2x0 + 0,
      
      [a#](x0) = x0 + 0,
      
      [b#](x0) = x0,
      
      [a](x0) = 2x0 + 0,
      
      [c](x0) = 2x0 + 0
     orientation:
      a#(a(x1)) = 2x1 + 0 >= x1 + 0 = c#(x1)
      
      a#(a(x1)) = 2x1 + 0 >= 2x1 + 0 = b#(c(x1))
      
      b#(b(x1)) = 2x1 + 0 >= x1 + 0 = c#(x1)
      
      b#(b(x1)) = 2x1 + 0 >= 2x1 + 0 = a#(c(x1))
      
      c#(c(x1)) = 2x1 + 0 >= x1 = b#(x1)
      
      c#(c(x1)) = 2x1 + 0 >= 2x1 + 0 = a#(b(x1))
      
      a(a(x1)) = 4x1 + 2 >= 4x1 + 2 = b(c(x1))
      
      b(b(x1)) = 4x1 + 2 >= 4x1 + 2 = a(c(x1))
      
      c(c(x1)) = 4x1 + 2 >= 4x1 + 2 = a(b(x1))
     problem:
      DPs:
       a#(a(x1)) -> c#(x1)
       a#(a(x1)) -> b#(c(x1))
       b#(b(x1)) -> c#(x1)
       b#(b(x1)) -> a#(c(x1))
       c#(c(x1)) -> a#(b(x1))
      TRS:
       a(a(x1)) -> b(c(x1))
       b(b(x1)) -> a(c(x1))
       c(c(x1)) -> a(b(x1))
     Restore Modifier:
      DPs:
       a#(a(x1)) -> c#(x1)
       a#(a(x1)) -> b#(c(x1))
       b#(b(x1)) -> c#(x1)
       b#(b(x1)) -> a#(c(x1))
       c#(c(x1)) -> a#(b(x1))
      TRS:
       a(a(x1)) -> b(c(x1))
       b(b(x1)) -> a(c(x1))
       c(c(x1)) -> a(b(x1))
      EDG Processor:
       DPs:
        a#(a(x1)) -> c#(x1)
        a#(a(x1)) -> b#(c(x1))
        b#(b(x1)) -> c#(x1)
        b#(b(x1)) -> a#(c(x1))
        c#(c(x1)) -> a#(b(x1))
       TRS:
        a(a(x1)) -> b(c(x1))
        b(b(x1)) -> a(c(x1))
        c(c(x1)) -> a(b(x1))
       graph:
        b#(b(x1)) -> c#(x1) -> c#(c(x1)) -> a#(b(x1))
        b#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> c#(x1)
        b#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> b#(c(x1))
        c#(c(x1)) -> a#(b(x1)) -> a#(a(x1)) -> c#(x1)
        c#(c(x1)) -> a#(b(x1)) -> a#(a(x1)) -> b#(c(x1))
        a#(a(x1)) -> b#(c(x1)) -> b#(b(x1)) -> c#(x1)
        a#(a(x1)) -> b#(c(x1)) -> b#(b(x1)) -> a#(c(x1))
        a#(a(x1)) -> c#(x1) -> c#(c(x1)) -> a#(b(x1))
       Arctic Interpretation Processor:
        dimension: 1
        usable rules:
         a(a(x1)) -> b(c(x1))
         b(b(x1)) -> a(c(x1))
         c(c(x1)) -> a(b(x1))
        interpretation:
         [c#](x0) = 1x0,
         
         [b](x0) = 1x0,
         
         [a#](x0) = x0,
         
         [b#](x0) = x0,
         
         [a](x0) = 1x0,
         
         [c](x0) = 1x0
        orientation:
         a#(a(x1)) = 1x1 >= 1x1 = c#(x1)
         
         a#(a(x1)) = 1x1 >= 1x1 = b#(c(x1))
         
         b#(b(x1)) = 1x1 >= 1x1 = c#(x1)
         
         b#(b(x1)) = 1x1 >= 1x1 = a#(c(x1))
         
         c#(c(x1)) = 2x1 >= 1x1 = a#(b(x1))
         
         a(a(x1)) = 2x1 >= 2x1 = b(c(x1))
         
         b(b(x1)) = 2x1 >= 2x1 = a(c(x1))
         
         c(c(x1)) = 2x1 >= 2x1 = a(b(x1))
        problem:
         DPs:
          a#(a(x1)) -> c#(x1)
          a#(a(x1)) -> b#(c(x1))
          b#(b(x1)) -> c#(x1)
          b#(b(x1)) -> a#(c(x1))
         TRS:
          a(a(x1)) -> b(c(x1))
          b(b(x1)) -> a(c(x1))
          c(c(x1)) -> a(b(x1))
        Restore Modifier:
         DPs:
          a#(a(x1)) -> c#(x1)
          a#(a(x1)) -> b#(c(x1))
          b#(b(x1)) -> c#(x1)
          b#(b(x1)) -> a#(c(x1))
         TRS:
          a(a(x1)) -> b(c(x1))
          b(b(x1)) -> a(c(x1))
          c(c(x1)) -> a(b(x1))
         EDG Processor:
          DPs:
           a#(a(x1)) -> c#(x1)
           a#(a(x1)) -> b#(c(x1))
           b#(b(x1)) -> c#(x1)
           b#(b(x1)) -> a#(c(x1))
          TRS:
           a(a(x1)) -> b(c(x1))
           b(b(x1)) -> a(c(x1))
           c(c(x1)) -> a(b(x1))
          graph:
           b#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> b#(c(x1))
           b#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> c#(x1)
           a#(a(x1)) -> b#(c(x1)) -> b#(b(x1)) -> a#(c(x1))
           a#(a(x1)) -> b#(c(x1)) -> b#(b(x1)) -> c#(x1)
          SCC Processor:
           #sccs: 1
           #rules: 2
           #arcs: 4/16
           DPs:
            b#(b(x1)) -> a#(c(x1))
            a#(a(x1)) -> b#(c(x1))
           TRS:
            a(a(x1)) -> b(c(x1))
            b(b(x1)) -> a(c(x1))
            c(c(x1)) -> a(b(x1))
           Arctic Interpretation Processor:
            dimension: 2
            usable rules:
             a(a(x1)) -> b(c(x1))
             b(b(x1)) -> a(c(x1))
             c(c(x1)) -> a(b(x1))
            interpretation:
                       [-& 0 ]     [0]
             [b](x0) = [0  2 ]x0 + [3],
             
             [a#](x0) = [-& -2]x0 + [2],
             
             [b#](x0) = [-& 0 ]x0 + [0],
             
                       [0  0 ]     [2 ]
             [a](x0) = [2  -4]x0 + [-4],
             
                       [0  2 ]     [0]
             [c](x0) = [0  -&]x0 + [2]
            orientation:
             b#(b(x1)) = [0 2]x1 + [3] >= [-2 -&]x1 + [2] = a#(c(x1))
             
             a#(a(x1)) = [0  -6]x1 + [2] >= [0  -&]x1 + [2] = b#(c(x1))
             
                        [2 0]     [2]    [0  -&]     [2]           
             a(a(x1)) = [2 2]x1 + [4] >= [2  2 ]x1 + [4] = b(c(x1))
             
                        [0 2]     [3]    [0 2]     [2]           
             b(b(x1)) = [2 4]x1 + [5] >= [2 4]x1 + [2] = a(c(x1))
             
                        [2 2]     [4]    [0  2 ]     [3]           
             c(c(x1)) = [0 2]x1 + [2] >= [-4 2 ]x1 + [2] = a(b(x1))
            problem:
             DPs:
              a#(a(x1)) -> b#(c(x1))
             TRS:
              a(a(x1)) -> b(c(x1))
              b(b(x1)) -> a(c(x1))
              c(c(x1)) -> a(b(x1))
            Restore Modifier:
             DPs:
              a#(a(x1)) -> b#(c(x1))
             TRS:
              a(a(x1)) -> b(c(x1))
              b(b(x1)) -> a(c(x1))
              c(c(x1)) -> a(b(x1))
             EDG Processor:
              DPs:
               a#(a(x1)) -> b#(c(x1))
              TRS:
               a(a(x1)) -> b(c(x1))
               b(b(x1)) -> a(c(x1))
               c(c(x1)) -> a(b(x1))
              graph:
               
              SCC Processor:
               #sccs: 0
               #rules: 0
               #arcs: 0/1