YES

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

Proof:
 DP Processor:
  DPs:
   b#(a(b(b(b(b(x1)))))) -> b#(a(x1))
   b#(a(b(b(b(b(x1)))))) -> b#(b(a(x1)))
   b#(a(b(b(b(b(x1)))))) -> b#(b(b(a(x1))))
   b#(a(b(b(b(b(x1)))))) -> b#(b(b(b(a(x1)))))
   b#(a(b(b(b(b(x1)))))) -> b#(b(b(b(b(a(x1))))))
  TRS:
   b(a(b(b(b(b(x1)))))) -> a(b(b(b(b(b(a(x1)))))))
  Arctic Interpretation Processor:
   dimension: 1
   interpretation:
    [b#](x0) = x0,
    
    [a](x0) = x0,
    
    [b](x0) = 2x0
   orientation:
    b#(a(b(b(b(b(x1)))))) = 8x1 >= x1 = b#(a(x1))
    
    b#(a(b(b(b(b(x1)))))) = 8x1 >= 2x1 = b#(b(a(x1)))
    
    b#(a(b(b(b(b(x1)))))) = 8x1 >= 4x1 = b#(b(b(a(x1))))
    
    b#(a(b(b(b(b(x1)))))) = 8x1 >= 6x1 = b#(b(b(b(a(x1)))))
    
    b#(a(b(b(b(b(x1)))))) = 8x1 >= 8x1 = b#(b(b(b(b(a(x1))))))
    
    b(a(b(b(b(b(x1)))))) = 10x1 >= 10x1 = a(b(b(b(b(b(a(x1)))))))
   problem:
    DPs:
     b#(a(b(b(b(b(x1)))))) -> b#(b(b(b(b(a(x1))))))
    TRS:
     b(a(b(b(b(b(x1)))))) -> a(b(b(b(b(b(a(x1)))))))
   Matrix Interpretation Processor: dim=3
    
    interpretation:
     [b#](x0) = [1 0 0]x0,
     
               [0 0 1]  
     [a](x0) = [0 0 0]x0
               [0 0 1]  ,
     
               [0 0 1]     [0]
     [b](x0) = [0 0 0]x0 + [1]
               [1 1 0]     [0]
    orientation:
     b#(a(b(b(b(b(x1)))))) = [0 0 1]x1 + [2] >= [0 0 1]x1 + [1] = b#(b(b(b(b(a(x1))))))
     
                            [0 0 1]     [2]    [0 0 1]     [2]                          
     b(a(b(b(b(b(x1)))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [0] = a(b(b(b(b(b(a(x1)))))))
                            [0 0 1]     [2]    [0 0 1]     [2]                          
    problem:
     DPs:
      
     TRS:
      b(a(b(b(b(b(x1)))))) -> a(b(b(b(b(b(a(x1)))))))
    Qed