YES

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

Proof:
 String Reversal Processor:
  a(a(a(x1))) -> b(a(a(x1)))
  b(a(b(x1))) -> a(b(a(x1)))
  DP Processor:
   DPs:
    a#(a(a(x1))) -> b#(a(a(x1)))
    b#(a(b(x1))) -> a#(x1)
    b#(a(b(x1))) -> b#(a(x1))
    b#(a(b(x1))) -> a#(b(a(x1)))
   TRS:
    a(a(a(x1))) -> b(a(a(x1)))
    b(a(b(x1))) -> a(b(a(x1)))
   TDG Processor:
    DPs:
     a#(a(a(x1))) -> b#(a(a(x1)))
     b#(a(b(x1))) -> a#(x1)
     b#(a(b(x1))) -> b#(a(x1))
     b#(a(b(x1))) -> a#(b(a(x1)))
    TRS:
     a(a(a(x1))) -> b(a(a(x1)))
     b(a(b(x1))) -> a(b(a(x1)))
    graph:
     b#(a(b(x1))) -> b#(a(x1)) -> b#(a(b(x1))) -> a#(b(a(x1)))
     b#(a(b(x1))) -> b#(a(x1)) -> b#(a(b(x1))) -> b#(a(x1))
     b#(a(b(x1))) -> b#(a(x1)) -> b#(a(b(x1))) -> a#(x1)
     b#(a(b(x1))) -> a#(b(a(x1))) -> a#(a(a(x1))) -> b#(a(a(x1)))
     b#(a(b(x1))) -> a#(x1) -> a#(a(a(x1))) -> b#(a(a(x1)))
     a#(a(a(x1))) -> b#(a(a(x1))) -> b#(a(b(x1))) -> a#(b(a(x1)))
     a#(a(a(x1))) -> b#(a(a(x1))) -> b#(a(b(x1))) -> b#(a(x1))
     a#(a(a(x1))) -> b#(a(a(x1))) -> b#(a(b(x1))) -> a#(x1)
    Arctic Interpretation Processor:
     dimension: 1
     interpretation:
      [b#](x0) = 5x0 + 0,
      
      [a#](x0) = 5x0 + 8,
      
      [b](x0) = 1x0 + 2,
      
      [a](x0) = 1x0 + 0
     orientation:
      a#(a(a(x1))) = 7x1 + 8 >= 7x1 + 6 = b#(a(a(x1)))
      
      b#(a(b(x1))) = 7x1 + 8 >= 5x1 + 8 = a#(x1)
      
      b#(a(b(x1))) = 7x1 + 8 >= 6x1 + 5 = b#(a(x1))
      
      b#(a(b(x1))) = 7x1 + 8 >= 7x1 + 8 = a#(b(a(x1)))
      
      a(a(a(x1))) = 3x1 + 2 >= 3x1 + 2 = b(a(a(x1)))
      
      b(a(b(x1))) = 3x1 + 4 >= 3x1 + 3 = a(b(a(x1)))
     problem:
      DPs:
       a#(a(a(x1))) -> b#(a(a(x1)))
       b#(a(b(x1))) -> a#(x1)
       b#(a(b(x1))) -> a#(b(a(x1)))
      TRS:
       a(a(a(x1))) -> b(a(a(x1)))
       b(a(b(x1))) -> a(b(a(x1)))
     EDG Processor:
      DPs:
       a#(a(a(x1))) -> b#(a(a(x1)))
       b#(a(b(x1))) -> a#(x1)
       b#(a(b(x1))) -> a#(b(a(x1)))
      TRS:
       a(a(a(x1))) -> b(a(a(x1)))
       b(a(b(x1))) -> a(b(a(x1)))
      graph:
       b#(a(b(x1))) -> a#(b(a(x1))) -> a#(a(a(x1))) -> b#(a(a(x1)))
       b#(a(b(x1))) -> a#(x1) -> a#(a(a(x1))) -> b#(a(a(x1)))
       a#(a(a(x1))) -> b#(a(a(x1))) -> b#(a(b(x1))) -> a#(x1)
       a#(a(a(x1))) -> b#(a(a(x1))) -> b#(a(b(x1))) -> a#(b(a(x1)))
      Arctic Interpretation Processor:
       dimension: 1
       interpretation:
        [b#](x0) = x0 + -16,
        
        [a#](x0) = x0 + 9,
        
        [b](x0) = 1x0 + 9,
        
        [a](x0) = 1x0 + 7
       orientation:
        a#(a(a(x1))) = 2x1 + 9 >= 2x1 + 8 = b#(a(a(x1)))
        
        b#(a(b(x1))) = 2x1 + 10 >= x1 + 9 = a#(x1)
        
        b#(a(b(x1))) = 2x1 + 10 >= 2x1 + 9 = a#(b(a(x1)))
        
        a(a(a(x1))) = 3x1 + 9 >= 3x1 + 9 = b(a(a(x1)))
        
        b(a(b(x1))) = 3x1 + 11 >= 3x1 + 10 = a(b(a(x1)))
       problem:
        DPs:
         a#(a(a(x1))) -> b#(a(a(x1)))
         b#(a(b(x1))) -> a#(b(a(x1)))
        TRS:
         a(a(a(x1))) -> b(a(a(x1)))
         b(a(b(x1))) -> a(b(a(x1)))
       EDG Processor:
        DPs:
         a#(a(a(x1))) -> b#(a(a(x1)))
         b#(a(b(x1))) -> a#(b(a(x1)))
        TRS:
         a(a(a(x1))) -> b(a(a(x1)))
         b(a(b(x1))) -> a(b(a(x1)))
        graph:
         b#(a(b(x1))) -> a#(b(a(x1))) -> a#(a(a(x1))) -> b#(a(a(x1)))
         a#(a(a(x1))) -> b#(a(a(x1))) -> b#(a(b(x1))) -> a#(b(a(x1)))
        Arctic Interpretation Processor:
         dimension: 3
         interpretation:
          [b#](x0) = [-& -& 0 ]x0 + [0],
          
          [a#](x0) = [-& 1  0 ]x0 + [0],
          
                    [1  1  0 ]     [1]
          [b](x0) = [-& -& 0 ]x0 + [0]
                    [0  0  1 ]     [1],
          
                    [-& 1  0 ]     [0]
          [a](x0) = [-& 1  0 ]x0 + [0]
                    [0  0  -&]     [0]
         orientation:
          a#(a(a(x1))) = [1 3 2]x1 + [2] >= [-& 1  0 ]x1 + [0] = b#(a(a(x1)))
          
          b#(a(b(x1))) = [1 1 0]x1 + [1] >= [1 1 0]x1 + [1] = a#(b(a(x1)))
          
                        [1 3 2]     [2]    [1  3  2 ]     [2]              
          a(a(a(x1))) = [1 3 2]x1 + [2] >= [-& 1  0 ]x1 + [0] = b(a(a(x1)))
                        [0 2 1]     [1]    [0  2  1 ]     [1]              
          
                        [1 1 2]     [2]    [1 1 0]     [1]              
          b(a(b(x1))) = [1 1 0]x1 + [1] >= [1 1 0]x1 + [1] = a(b(a(x1)))
                        [2 2 1]     [2]    [0 2 1]     [1]              
         problem:
          DPs:
           b#(a(b(x1))) -> a#(b(a(x1)))
          TRS:
           a(a(a(x1))) -> b(a(a(x1)))
           b(a(b(x1))) -> a(b(a(x1)))
         EDG Processor:
          DPs:
           b#(a(b(x1))) -> a#(b(a(x1)))
          TRS:
           a(a(a(x1))) -> b(a(a(x1)))
           b(a(b(x1))) -> a(b(a(x1)))
          graph:
           
          Qed