YES

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

Proof:
 String Reversal Processor:
  a(a(x1)) -> x1
  b(a(x1)) -> c(x1)
  c(c(x1)) -> a(a(b(c(b(x1)))))
  DP Processor:
   DPs:
    b#(a(x1)) -> c#(x1)
    c#(c(x1)) -> b#(x1)
    c#(c(x1)) -> c#(b(x1))
    c#(c(x1)) -> b#(c(b(x1)))
    c#(c(x1)) -> a#(b(c(b(x1))))
    c#(c(x1)) -> a#(a(b(c(b(x1)))))
   TRS:
    a(a(x1)) -> x1
    b(a(x1)) -> c(x1)
    c(c(x1)) -> a(a(b(c(b(x1)))))
   TDG Processor:
    DPs:
     b#(a(x1)) -> c#(x1)
     c#(c(x1)) -> b#(x1)
     c#(c(x1)) -> c#(b(x1))
     c#(c(x1)) -> b#(c(b(x1)))
     c#(c(x1)) -> a#(b(c(b(x1))))
     c#(c(x1)) -> a#(a(b(c(b(x1)))))
    TRS:
     a(a(x1)) -> x1
     b(a(x1)) -> c(x1)
     c(c(x1)) -> a(a(b(c(b(x1)))))
    graph:
     c#(c(x1)) -> c#(b(x1)) -> c#(c(x1)) -> a#(a(b(c(b(x1)))))
     c#(c(x1)) -> c#(b(x1)) -> c#(c(x1)) -> a#(b(c(b(x1))))
     c#(c(x1)) -> c#(b(x1)) -> c#(c(x1)) -> b#(c(b(x1)))
     c#(c(x1)) -> c#(b(x1)) -> c#(c(x1)) -> c#(b(x1))
     c#(c(x1)) -> c#(b(x1)) -> c#(c(x1)) -> b#(x1)
     c#(c(x1)) -> b#(c(b(x1))) -> b#(a(x1)) -> c#(x1)
     c#(c(x1)) -> b#(x1) -> b#(a(x1)) -> c#(x1)
     b#(a(x1)) -> c#(x1) -> c#(c(x1)) -> a#(a(b(c(b(x1)))))
     b#(a(x1)) -> c#(x1) -> c#(c(x1)) -> a#(b(c(b(x1))))
     b#(a(x1)) -> c#(x1) -> c#(c(x1)) -> b#(c(b(x1)))
     b#(a(x1)) -> c#(x1) -> c#(c(x1)) -> c#(b(x1))
     b#(a(x1)) -> c#(x1) -> c#(c(x1)) -> b#(x1)
    SCC Processor:
     #sccs: 1
     #rules: 4
     #arcs: 12/36
     DPs:
      c#(c(x1)) -> c#(b(x1))
      c#(c(x1)) -> b#(x1)
      b#(a(x1)) -> c#(x1)
      c#(c(x1)) -> b#(c(b(x1)))
     TRS:
      a(a(x1)) -> x1
      b(a(x1)) -> c(x1)
      c(c(x1)) -> a(a(b(c(b(x1)))))
     Arctic Interpretation Processor:
      dimension: 2
      interpretation:
       [c#](x0) = [0 1]x0,
       
       [b#](x0) = [1 0]x0 + [0],
       
                 [-& -&]     [0]
       [c](x0) = [0  0 ]x0 + [1],
       
                 [0  -&]     [0]
       [b](x0) = [0  0 ]x0 + [1],
       
                 [-& 0 ]     [0]
       [a](x0) = [0  -&]x0 + [0]
      orientation:
       c#(c(x1)) = [1 1]x1 + [2] >= [1 1]x1 + [2] = c#(b(x1))
       
       c#(c(x1)) = [1 1]x1 + [2] >= [1 0]x1 + [0] = b#(x1)
       
       b#(a(x1)) = [0 1]x1 + [1] >= [0 1]x1 = c#(x1)
       
       c#(c(x1)) = [1 1]x1 + [2] >= [0 0]x1 + [1] = b#(c(b(x1)))
       
                       [0]           
       a(a(x1)) = x1 + [0] >= x1 = x1
       
                  [-& 0 ]     [0]    [-& -&]     [0]        
       b(a(x1)) = [0  0 ]x1 + [1] >= [0  0 ]x1 + [1] = c(x1)
       
                  [-& -&]     [0]    [-& -&]     [0]                    
       c(c(x1)) = [0  0 ]x1 + [1] >= [0  0 ]x1 + [1] = a(a(b(c(b(x1)))))
      problem:
       DPs:
        c#(c(x1)) -> c#(b(x1))
        c#(c(x1)) -> b#(x1)
        b#(a(x1)) -> c#(x1)
       TRS:
        a(a(x1)) -> x1
        b(a(x1)) -> c(x1)
        c(c(x1)) -> a(a(b(c(b(x1)))))
      EDG Processor:
       DPs:
        c#(c(x1)) -> c#(b(x1))
        c#(c(x1)) -> b#(x1)
        b#(a(x1)) -> c#(x1)
       TRS:
        a(a(x1)) -> x1
        b(a(x1)) -> c(x1)
        c(c(x1)) -> a(a(b(c(b(x1)))))
       graph:
        c#(c(x1)) -> c#(b(x1)) -> c#(c(x1)) -> b#(x1)
        c#(c(x1)) -> c#(b(x1)) -> c#(c(x1)) -> c#(b(x1))
        c#(c(x1)) -> b#(x1) -> b#(a(x1)) -> c#(x1)
        b#(a(x1)) -> c#(x1) -> c#(c(x1)) -> b#(x1)
        b#(a(x1)) -> c#(x1) -> c#(c(x1)) -> c#(b(x1))
       Arctic Interpretation Processor:
        dimension: 3
        interpretation:
         [c#](x0) = [1 0 0]x0 + [1],
         
         [b#](x0) = [0 0 0]x0 + [0],
         
                   [0  1  0 ]     [1]
         [c](x0) = [1  0  -&]x0 + [0]
                   [0  -& -&]     [0],
         
                   [-& 0  -&]     [0]
         [b](x0) = [-& -& 0 ]x0 + [0]
                   [-& 0  1 ]     [1],
         
                   [-& 0  -&]     [0]
         [a](x0) = [0  1  0 ]x0 + [1]
                   [1  0  -&]     [1]
        orientation:
         c#(c(x1)) = [1 2 1]x1 + [2] >= [-& 1  1 ]x1 + [1] = c#(b(x1))
         
         c#(c(x1)) = [1 2 1]x1 + [2] >= [0 0 0]x1 + [0] = b#(x1)
         
         b#(a(x1)) = [1 1 0]x1 + [1] >= [1 0 0]x1 + [1] = c#(x1)
         
                    [0 1 0]     [1]           
         a(a(x1)) = [1 2 1]x1 + [2] >= x1 = x1
                    [0 1 0]     [1]           
         
                    [0  1  0 ]     [1]    [0  1  0 ]     [1]        
         b(a(x1)) = [1  0  -&]x1 + [1] >= [1  0  -&]x1 + [0] = c(x1)
                    [2  1  0 ]     [2]    [0  -& -&]     [0]        
         
                    [2 1 0]     [1]    [-& 1  0 ]     [1]                    
         c(c(x1)) = [1 2 1]x1 + [2] >= [-& 2  1 ]x1 + [2] = a(a(b(c(b(x1)))))
                    [0 1 0]     [1]    [-& 1  0 ]     [1]                    
        problem:
         DPs:
          c#(c(x1)) -> c#(b(x1))
          b#(a(x1)) -> c#(x1)
         TRS:
          a(a(x1)) -> x1
          b(a(x1)) -> c(x1)
          c(c(x1)) -> a(a(b(c(b(x1)))))
        EDG Processor:
         DPs:
          c#(c(x1)) -> c#(b(x1))
          b#(a(x1)) -> c#(x1)
         TRS:
          a(a(x1)) -> x1
          b(a(x1)) -> c(x1)
          c(c(x1)) -> a(a(b(c(b(x1)))))
         graph:
          c#(c(x1)) -> c#(b(x1)) -> c#(c(x1)) -> c#(b(x1))
          b#(a(x1)) -> c#(x1) -> c#(c(x1)) -> c#(b(x1))
         SCC Processor:
          #sccs: 1
          #rules: 1
          #arcs: 2/4
          DPs:
           c#(c(x1)) -> c#(b(x1))
          TRS:
           a(a(x1)) -> x1
           b(a(x1)) -> c(x1)
           c(c(x1)) -> a(a(b(c(b(x1)))))
          Arctic Interpretation Processor:
           dimension: 3
           interpretation:
            [c#](x0) = [0 0 1]x0 + [0],
            
                      [-& -& 0 ]     [0]
            [c](x0) = [-& 0  1 ]x0 + [0]
                      [0  1  0 ]     [1],
            
                      [0  0  -&]     [0]
            [b](x0) = [0  -& -&]x0 + [0]
                      [-& 0  -&]     [0],
            
                      [-& 0  1 ]     [1 ]
            [a](x0) = [0  1  0 ]x0 + [1 ]
                      [-& 0  -&]     [-&]
           orientation:
            c#(c(x1)) = [1 2 1]x1 + [2] >= [0  1  -&]x1 + [1] = c#(b(x1))
            
                       [0 1 0]     [1]           
            a(a(x1)) = [1 2 1]x1 + [2] >= x1 = x1
                       [0 1 0]     [1]           
            
                       [0  1  1 ]     [1]    [-& -& 0 ]     [0]        
            b(a(x1)) = [-& 0  1 ]x1 + [1] >= [-& 0  1 ]x1 + [0] = c(x1)
                       [0  1  0 ]     [1]    [0  1  0 ]     [1]        
            
                       [0 1 0]     [1]    [0  1  -&]     [1]                    
            c(c(x1)) = [1 2 1]x1 + [2] >= [1  2  -&]x1 + [2] = a(a(b(c(b(x1)))))
                       [0 1 2]     [1]    [0  1  -&]     [1]                    
           problem:
            DPs:
             
            TRS:
             a(a(x1)) -> x1
             b(a(x1)) -> c(x1)
             c(c(x1)) -> a(a(b(c(b(x1)))))
           Qed