YES

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

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