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: 1
     interpretation:
      [b#](x0) = 1x0 + 15,
      
      [a#](x0) = 1x0 + 15,
      
      [b](x0) = 2x0 + 13,
      
      [a](x0) = 2x0 + 13
     orientation:
      a#(b(x1)) = 3x1 + 15 >= 3x1 + 15 = b#(b(x1))
      
      b#(a(b(x1))) = 5x1 + 16 >= 5x1 + 16 = a#(a(b(x1)))
      
      a#(a(a(x1))) = 5x1 + 16 >= 3x1 + 15 = b#(a(x1))
      
      a#(a(a(x1))) = 5x1 + 16 >= 5x1 + 16 = b#(b(a(x1)))
      
      a(b(x1)) = 4x1 + 15 >= 4x1 + 15 = b(b(x1))
      
      b(a(b(x1))) = 6x1 + 17 >= 6x1 + 17 = a(a(b(x1)))
      
      a(a(a(x1))) = 6x1 + 17 >= 6x1 + 17 = 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)))
     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
       interpretation:
        [b#](x0) = [-& 0 ]x0 + [0],
        
        [a#](x0) = [0 0]x0 + [0],
        
                  [1 2]     [2]
        [b](x0) = [0 1]x0 + [1],
        
                  [0 2]     [0]
        [a](x0) = [2 1]x0 + [1]
       orientation:
        a#(b(x1)) = [1 2]x1 + [2] >= [0 1]x1 + [1] = b#(b(x1))
        
        b#(a(b(x1))) = [3 4]x1 + [4] >= [3 4]x1 + [4] = a#(a(b(x1)))
        
        a#(a(a(x1))) = [4 4]x1 + [3] >= [3 2]x1 + [2] = b#(b(a(x1)))
        
                   [2 3]     [3]    [2 3]     [3]           
        a(b(x1)) = [3 4]x1 + [4] >= [1 2]x1 + [2] = b(b(x1))
        
                      [5 6]     [6]    [5 6]     [6]              
        b(a(b(x1))) = [4 5]x1 + [5] >= [4 5]x1 + [5] = a(a(b(x1)))
        
                      [5 6]     [4]    [5 4]     [4]              
        a(a(a(x1))) = [6 5]x1 + [5] >= [4 3]x1 + [3] = b(b(a(x1)))
       problem:
        DPs:
         b#(a(b(x1))) -> a#(a(b(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:
         b#(a(b(x1))) -> a#(a(b(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