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
     interpretation:
      [c#](x0) = x0,
      
      [b#](x0) = x0,
      
      [a#](x0) = x0,
      
      [c](x0) = 1x0,
      
      [b](x0) = 1x0,
      
      [a](x0) = 1x0
     orientation:
      a#(a(x1)) = 1x1 >= x1 = b#(x1)
      
      a#(a(x1)) = 1x1 >= 1x1 = b#(b(x1))
      
      b#(a(x1)) = 1x1 >= x1 = c#(x1)
      
      b#(a(x1)) = 1x1 >= 1x1 = c#(c(x1))
      
      c#(b(x1)) = 1x1 >= x1 = a#(x1)
      
      c#(b(x1)) = 1x1 >= 1x1 = a#(a(x1))
      
      a(a(x1)) = 2x1 >= 2x1 = b(b(x1))
      
      b(a(x1)) = 2x1 >= 2x1 = c(c(x1))
      
      c(b(x1)) = 2x1 >= 2x1 = 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))
     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
       interpretation:
        [c#](x0) = [0 1 0]x0 + [0],
        
        [b#](x0) = [0 0 0]x0 + [0],
        
        [a#](x0) = [1  1  -&]x0 + [0],
        
                  [0  1  0 ]     [-&]
        [c](x0) = [0  0  -&]x0 + [-&]
                  [0  1  0 ]     [0 ],
        
                  [0 0 0]     [0]
        [b](x0) = [0 0 0]x0 + [0]
                  [0 0 0]     [0],
        
                  [0  -& 0 ]     [0]
        [a](x0) = [0  0  -&]x0 + [0]
                  [1  1  0 ]     [0]
       orientation:
        a#(a(x1)) = [1 1 1]x1 + [1] >= [0 0 0]x1 + [0] = b#(b(x1))
        
        b#(a(x1)) = [1 1 0]x1 + [0] >= [1 1 0]x1 + [0] = c#(c(x1))
        
        c#(b(x1)) = [1 1 1]x1 + [1] >= [1 1 1]x1 + [1] = a#(a(x1))
        
                   [1 1 0]     [0]    [0 0 0]     [0]           
        a(a(x1)) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = b(b(x1))
                   [1 1 1]     [1]    [0 0 0]     [0]           
        
                   [1 1 0]     [0]    [1 1 0]     [0 ]           
        b(a(x1)) = [1 1 0]x1 + [0] >= [0 1 0]x1 + [-&] = c(c(x1))
                   [1 1 0]     [0]    [1 1 0]     [0 ]           
        
                   [1 1 1]     [1]    [1 1 0]     [0]           
        c(b(x1)) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = a(a(x1))
                   [1 1 1]     [1]    [1 1 1]     [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))
       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