YES

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

Proof:
 String Reversal Processor:
  b(b(x1)) -> b(a(b(x1)))
  b(a(b(b(x1)))) -> b(b(a(a(b(a(b(x1)))))))
  b(a(b(x1))) -> b(a(a(b(x1))))
  b(a(b(a(a(b(x1)))))) -> b(b(x1))
  Matrix Interpretation Processor: dim=3
   
   interpretation:
              [1 0 0]  
    [a](x0) = [0 0 0]x0
              [0 1 0]  ,
    
              [1 1 1]     [0]
    [b](x0) = [0 0 0]x0 + [1]
              [0 0 0]     [0]
   orientation:
               [1 1 1]     [1]    [1 1 1]     [1]              
    b(b(x1)) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(a(b(x1)))
               [0 0 0]     [0]    [0 0 0]     [0]              
    
                     [1 1 1]     [2]    [1 1 1]     [2]                          
    b(a(b(b(x1)))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(b(a(a(b(a(b(x1)))))))
                     [0 0 0]     [0]    [0 0 0]     [0]                          
    
                  [1 1 1]     [1]    [1 1 1]     [0]                 
    b(a(b(x1))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(a(a(b(x1))))
                  [0 0 0]     [0]    [0 0 0]     [0]                 
    
                           [1 1 1]     [1]    [1 1 1]     [1]           
    b(a(b(a(a(b(x1)))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(b(x1))
                           [0 0 0]     [0]    [0 0 0]     [0]           
   problem:
    b(b(x1)) -> b(a(b(x1)))
    b(a(b(b(x1)))) -> b(b(a(a(b(a(b(x1)))))))
    b(a(b(a(a(b(x1)))))) -> b(b(x1))
   String Reversal Processor:
    b(b(x1)) -> b(a(b(x1)))
    b(b(a(b(x1)))) -> b(a(b(a(a(b(b(x1)))))))
    b(a(a(b(a(b(x1)))))) -> b(b(x1))
    DP Processor:
     DPs:
      b#(b(x1)) -> b#(a(b(x1)))
      b#(b(a(b(x1)))) -> b#(b(x1))
      b#(b(a(b(x1)))) -> b#(a(a(b(b(x1)))))
      b#(b(a(b(x1)))) -> b#(a(b(a(a(b(b(x1)))))))
      b#(a(a(b(a(b(x1)))))) -> b#(b(x1))
     TRS:
      b(b(x1)) -> b(a(b(x1)))
      b(b(a(b(x1)))) -> b(a(b(a(a(b(b(x1)))))))
      b(a(a(b(a(b(x1)))))) -> b(b(x1))
     EDG Processor:
      DPs:
       b#(b(x1)) -> b#(a(b(x1)))
       b#(b(a(b(x1)))) -> b#(b(x1))
       b#(b(a(b(x1)))) -> b#(a(a(b(b(x1)))))
       b#(b(a(b(x1)))) -> b#(a(b(a(a(b(b(x1)))))))
       b#(a(a(b(a(b(x1)))))) -> b#(b(x1))
      TRS:
       b(b(x1)) -> b(a(b(x1)))
       b(b(a(b(x1)))) -> b(a(b(a(a(b(b(x1)))))))
       b(a(a(b(a(b(x1)))))) -> b(b(x1))
      graph:
       b#(a(a(b(a(b(x1)))))) -> b#(b(x1)) ->
       b#(b(x1)) -> b#(a(b(x1)))
       b#(a(a(b(a(b(x1)))))) -> b#(b(x1)) ->
       b#(b(a(b(x1)))) -> b#(b(x1))
       b#(a(a(b(a(b(x1)))))) -> b#(b(x1)) ->
       b#(b(a(b(x1)))) -> b#(a(a(b(b(x1)))))
       b#(a(a(b(a(b(x1)))))) -> b#(b(x1)) ->
       b#(b(a(b(x1)))) -> b#(a(b(a(a(b(b(x1)))))))
       b#(b(a(b(x1)))) -> b#(a(a(b(b(x1))))) ->
       b#(a(a(b(a(b(x1)))))) -> b#(b(x1))
       b#(b(a(b(x1)))) -> b#(b(x1)) -> b#(b(x1)) -> b#(a(b(x1)))
       b#(b(a(b(x1)))) -> b#(b(x1)) -> b#(b(a(b(x1)))) -> b#(b(x1))
       b#(b(a(b(x1)))) -> b#(b(x1)) ->
       b#(b(a(b(x1)))) -> b#(a(a(b(b(x1)))))
       b#(b(a(b(x1)))) -> b#(b(x1)) -> b#(b(a(b(x1)))) -> b#(a(b(a(a(b(b(x1)))))))
      SCC Processor:
       #sccs: 1
       #rules: 3
       #arcs: 9/25
       DPs:
        b#(a(a(b(a(b(x1)))))) -> b#(b(x1))
        b#(b(a(b(x1)))) -> b#(a(a(b(b(x1)))))
        b#(b(a(b(x1)))) -> b#(b(x1))
       TRS:
        b(b(x1)) -> b(a(b(x1)))
        b(b(a(b(x1)))) -> b(a(b(a(a(b(b(x1)))))))
        b(a(a(b(a(b(x1)))))) -> b(b(x1))
       Matrix Interpretation Processor: dim=4
        
        interpretation:
                   [0 0 0 1]  
                   [0 1 0 0]  
         [a](x0) = [0 0 0 0]x0
                   [1 0 1 0]  ,
         
                   [0 0 1 1]     [0]
                   [0 0 0 0]     [1]
         [b](x0) = [0 1 0 0]x0 + [0]
                   [0 0 1 1]     [0],
         
         [b#](x0) = [1 0 1 0]x0
        orientation:
         b#(a(a(b(a(b(x1)))))) = [0 1 1 1]x1 + [1] >= [0 1 1 1]x1 = b#(b(x1))
         
         b#(b(a(b(x1)))) = [0 1 1 1]x1 + [1] >= [0 1 1 1]x1 + [1] = b#(a(a(b(b(x1)))))
         
         b#(b(a(b(x1)))) = [0 1 1 1]x1 + [1] >= [0 1 1 1]x1 = b#(b(x1))
         
                    [0 1 1 1]     [0]    [0 1 1 1]     [0]              
                    [0 0 0 0]     [1]    [0 0 0 0]     [1]              
         b(b(x1)) = [0 0 0 0]x1 + [1] >= [0 0 0 0]x1 + [1] = b(a(b(x1)))
                    [0 1 1 1]     [0]    [0 1 1 1]     [0]              
         
                          [0 1 1 1]     [1]    [0 1 1 1]     [1]                          
                          [0 0 0 0]     [1]    [0 0 0 0]     [1]                          
         b(b(a(b(x1)))) = [0 0 0 0]x1 + [1] >= [0 0 0 0]x1 + [1] = b(a(b(a(a(b(b(x1)))))))
                          [0 1 1 1]     [1]    [0 1 1 1]     [1]                          
         
                                [0 1 1 1]     [0]    [0 1 1 1]     [0]           
                                [0 0 0 0]     [1]    [0 0 0 0]     [1]           
         b(a(a(b(a(b(x1)))))) = [0 0 0 0]x1 + [1] >= [0 0 0 0]x1 + [1] = b(b(x1))
                                [0 1 1 1]     [0]    [0 1 1 1]     [0]           
        problem:
         DPs:
          b#(b(a(b(x1)))) -> b#(a(a(b(b(x1)))))
         TRS:
          b(b(x1)) -> b(a(b(x1)))
          b(b(a(b(x1)))) -> b(a(b(a(a(b(b(x1)))))))
          b(a(a(b(a(b(x1)))))) -> b(b(x1))
        Restore Modifier:
         DPs:
          b#(b(a(b(x1)))) -> b#(a(a(b(b(x1)))))
         TRS:
          b(b(x1)) -> b(a(b(x1)))
          b(b(a(b(x1)))) -> b(a(b(a(a(b(b(x1)))))))
          b(a(a(b(a(b(x1)))))) -> b(b(x1))
         EDG Processor:
          DPs:
           b#(b(a(b(x1)))) -> b#(a(a(b(b(x1)))))
          TRS:
           b(b(x1)) -> b(a(b(x1)))
           b(b(a(b(x1)))) -> b(a(b(a(a(b(b(x1)))))))
           b(a(a(b(a(b(x1)))))) -> b(b(x1))
          graph:
           
          SCC Processor:
           #sccs: 0
           #rules: 0
           #arcs: 0/1