YES

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

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