YES

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

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