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