YES

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

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