YES

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

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