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: 2
     usable rules:
      a(a(a(x1))) -> b(a(a(x1)))
      b(a(b(x1))) -> a(b(a(x1)))
     interpretation:
      [b#](x0) = [-& 3 ]x0 + [0],
      
      [a#](x0) = [0 3]x0 + [0],
      
                [-& 0 ]     [0]
      [b](x0) = [0  1 ]x0 + [0],
      
                [0 0]     [0]
      [a](x0) = [0 1]x0 + [0]
     orientation:
      a#(a(a(x1))) = [4 5]x1 + [4] >= [4 5]x1 + [4] = b#(a(a(x1)))
      
      b#(a(b(x1))) = [4 5]x1 + [4] >= [0 3]x1 + [0] = a#(x1)
      
      b#(a(b(x1))) = [4 5]x1 + [4] >= [3 4]x1 + [3] = b#(a(x1))
      
      b#(a(b(x1))) = [4 5]x1 + [4] >= [4 5]x1 + [4] = a#(b(a(x1)))
      
                    [1 2]     [1]    [1 2]     [1]              
      a(a(a(x1))) = [2 3]x1 + [2] >= [2 3]x1 + [2] = b(a(a(x1)))
      
                    [1 2]     [1]    [1 2]     [1]              
      b(a(b(x1))) = [2 3]x1 + [2] >= [2 3]x1 + [2] = 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)))
     Restore Modifier:
      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
        usable rules:
         a(a(a(x1))) -> b(a(a(x1)))
         b(a(b(x1))) -> a(b(a(x1)))
        interpretation:
         [b#](x0) = [1  -& 0 ]x0 + [0],
         
         [a#](x0) = [-& 1  1 ]x0 + [0],
         
                   [1 0 1]     [0]
         [b](x0) = [1 0 0]x0 + [0]
                   [0 0 1]     [1],
         
                   [-& 0  1 ]     [1]
         [a](x0) = [1  1  0 ]x0 + [0]
                   [-& 0  -&]     [0]
        orientation:
         a#(a(a(x1))) = [3 3 3]x1 + [3] >= [2 2 1]x1 + [2] = b#(a(a(x1)))
         
         b#(a(b(x1))) = [2 2 3]x1 + [3] >= [2 2 3]x1 + [3] = a#(b(a(x1)))
         
                       [2 2 2]     [2]    [2 2 2]     [2]              
         a(a(a(x1))) = [3 3 3]x1 + [3] >= [2 2 2]x1 + [2] = b(a(a(x1)))
                       [2 2 2]     [2]    [2 2 2]     [2]              
         
                       [2 2 3]     [3]    [2 2 2]     [2]              
         b(a(b(x1))) = [2 2 3]x1 + [3] >= [2 2 3]x1 + [3] = a(b(a(x1)))
                       [2 1 2]     [2]    [1 1 2]     [2]              
        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)))
        Restore Modifier:
         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