YES

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

Proof:
 DP Processor:
  DPs:
   b#(b(a(b(b(b(x1)))))) -> b#(a(x1))
   b#(b(a(b(b(b(x1)))))) -> b#(b(a(x1)))
   b#(b(a(b(b(b(x1)))))) -> b#(b(b(a(x1))))
   b#(b(a(b(b(b(x1)))))) -> b#(b(b(b(a(x1)))))
   b#(b(a(b(b(b(x1)))))) -> b#(b(b(b(b(a(x1))))))
  TRS:
   b(b(a(b(b(b(x1)))))) -> a(b(b(b(b(b(a(x1)))))))
  Matrix Interpretation Processor: dim=3
   
   interpretation:
    [b#](x0) = [2 1 0]x0 + [1],
    
              [0 0 0]     [0]
    [a](x0) = [0 1 0]x0 + [0]
              [0 0 0]     [1],
    
              [0 0 1]     [0]
    [b](x0) = [0 1 0]x0 + [1]
              [1 0 0]     [0]
   orientation:
    b#(b(a(b(b(b(x1)))))) = [0 1 0]x1 + [7] >= [0 1 0]x1 + [1] = b#(a(x1))
    
    b#(b(a(b(b(b(x1)))))) = [0 1 0]x1 + [7] >= [0 1 0]x1 + [4] = b#(b(a(x1)))
    
    b#(b(a(b(b(b(x1)))))) = [0 1 0]x1 + [7] >= [0 1 0]x1 + [3] = b#(b(b(a(x1))))
    
    b#(b(a(b(b(b(x1)))))) = [0 1 0]x1 + [7] >= [0 1 0]x1 + [6] = b#(b(b(b(a(x1)))))
    
    b#(b(a(b(b(b(x1)))))) = [0 1 0]x1 + [7] >= [0 1 0]x1 + [5] = b#(b(b(b(b(a(x1))))))
    
                           [0 0 0]     [0]    [0 0 0]     [0]                          
    b(b(a(b(b(b(x1)))))) = [0 1 0]x1 + [5] >= [0 1 0]x1 + [5] = a(b(b(b(b(b(a(x1)))))))
                           [0 0 0]     [1]    [0 0 0]     [1]                          
   problem:
    DPs:
     
    TRS:
     b(b(a(b(b(b(x1)))))) -> a(b(b(b(b(b(a(x1)))))))
   Qed