YES

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

Proof:
 DP Processor:
  DPs:
   a#(b(a(b(a(a(a(x1))))))) -> a#(b(x1))
   a#(b(a(b(a(a(a(x1))))))) -> a#(b(a(b(x1))))
   a#(b(a(b(a(a(a(x1))))))) -> a#(b(a(b(a(b(x1))))))
   a#(b(a(b(a(a(a(x1))))))) -> a#(a(b(a(b(a(b(x1)))))))
   a#(b(a(b(a(a(a(x1))))))) -> a#(a(a(b(a(b(a(b(x1))))))))
   a#(b(a(b(a(a(a(x1))))))) -> a#(a(a(a(b(a(b(a(b(x1)))))))))
  TRS:
   a(b(a(b(a(a(a(x1))))))) -> a(a(a(a(b(a(b(a(b(x1)))))))))
  EDG Processor:
   DPs:
    a#(b(a(b(a(a(a(x1))))))) -> a#(b(x1))
    a#(b(a(b(a(a(a(x1))))))) -> a#(b(a(b(x1))))
    a#(b(a(b(a(a(a(x1))))))) -> a#(b(a(b(a(b(x1))))))
    a#(b(a(b(a(a(a(x1))))))) -> a#(a(b(a(b(a(b(x1)))))))
    a#(b(a(b(a(a(a(x1))))))) -> a#(a(a(b(a(b(a(b(x1))))))))
    a#(b(a(b(a(a(a(x1))))))) -> a#(a(a(a(b(a(b(a(b(x1)))))))))
   TRS:
    a(b(a(b(a(a(a(x1))))))) -> a(a(a(a(b(a(b(a(b(x1)))))))))
   graph:
    a#(b(a(b(a(a(a(x1))))))) -> a#(b(a(b(a(b(x1)))))) ->
    a#(b(a(b(a(a(a(x1))))))) -> a#(b(x1))
    a#(b(a(b(a(a(a(x1))))))) -> a#(b(a(b(a(b(x1)))))) ->
    a#(b(a(b(a(a(a(x1))))))) -> a#(b(a(b(x1))))
    a#(b(a(b(a(a(a(x1))))))) -> a#(b(a(b(a(b(x1)))))) ->
    a#(b(a(b(a(a(a(x1))))))) -> a#(b(a(b(a(b(x1))))))
    a#(b(a(b(a(a(a(x1))))))) -> a#(b(a(b(a(b(x1)))))) ->
    a#(b(a(b(a(a(a(x1))))))) -> a#(a(b(a(b(a(b(x1)))))))
    a#(b(a(b(a(a(a(x1))))))) -> a#(b(a(b(a(b(x1)))))) ->
    a#(b(a(b(a(a(a(x1))))))) -> a#(a(a(b(a(b(a(b(x1))))))))
    a#(b(a(b(a(a(a(x1))))))) -> a#(b(a(b(a(b(x1)))))) ->
    a#(b(a(b(a(a(a(x1))))))) -> a#(a(a(a(b(a(b(a(b(x1)))))))))
    a#(b(a(b(a(a(a(x1))))))) -> a#(b(a(b(x1)))) ->
    a#(b(a(b(a(a(a(x1))))))) -> a#(b(x1))
    a#(b(a(b(a(a(a(x1))))))) -> a#(b(a(b(x1)))) ->
    a#(b(a(b(a(a(a(x1))))))) -> a#(b(a(b(x1))))
    a#(b(a(b(a(a(a(x1))))))) -> a#(b(a(b(x1)))) ->
    a#(b(a(b(a(a(a(x1))))))) -> a#(b(a(b(a(b(x1))))))
    a#(b(a(b(a(a(a(x1))))))) -> a#(b(a(b(x1)))) ->
    a#(b(a(b(a(a(a(x1))))))) -> a#(a(b(a(b(a(b(x1)))))))
    a#(b(a(b(a(a(a(x1))))))) -> a#(b(a(b(x1)))) ->
    a#(b(a(b(a(a(a(x1))))))) -> a#(a(a(b(a(b(a(b(x1))))))))
    a#(b(a(b(a(a(a(x1))))))) -> a#(b(a(b(x1)))) ->
    a#(b(a(b(a(a(a(x1))))))) -> a#(a(a(a(b(a(b(a(b(x1)))))))))
    a#(b(a(b(a(a(a(x1))))))) -> a#(b(x1)) ->
    a#(b(a(b(a(a(a(x1))))))) -> a#(b(x1))
    a#(b(a(b(a(a(a(x1))))))) -> a#(b(x1)) ->
    a#(b(a(b(a(a(a(x1))))))) -> a#(b(a(b(x1))))
    a#(b(a(b(a(a(a(x1))))))) -> a#(b(x1)) ->
    a#(b(a(b(a(a(a(x1))))))) -> a#(b(a(b(a(b(x1))))))
    a#(b(a(b(a(a(a(x1))))))) -> a#(b(x1)) ->
    a#(b(a(b(a(a(a(x1))))))) -> a#(a(b(a(b(a(b(x1)))))))
    a#(b(a(b(a(a(a(x1))))))) -> a#(b(x1)) ->
    a#(b(a(b(a(a(a(x1))))))) -> a#(a(a(b(a(b(a(b(x1))))))))
    a#(b(a(b(a(a(a(x1))))))) -> a#(b(x1)) ->
    a#(b(a(b(a(a(a(x1))))))) -> a#(a(a(a(b(a(b(a(b(x1)))))))))
   SCC Processor:
    #sccs: 1
    #rules: 3
    #arcs: 18/36
    DPs:
     a#(b(a(b(a(a(a(x1))))))) -> a#(b(a(b(a(b(x1))))))
     a#(b(a(b(a(a(a(x1))))))) -> a#(b(a(b(x1))))
     a#(b(a(b(a(a(a(x1))))))) -> a#(b(x1))
    TRS:
     a(b(a(b(a(a(a(x1))))))) -> a(a(a(a(b(a(b(a(b(x1)))))))))
    Matrix Interpretation Processor: dim=3
     
     interpretation:
                [0 0 1]  
      [b](x0) = [0 0 1]x0
                [0 0 1]  ,
      
                [0 0 1]     [1]
      [a](x0) = [1 0 0]x0 + [1]
                [0 1 0]     [0],
      
      [a#](x0) = [0 1 0]x0 + [1]
     orientation:
      a#(b(a(b(a(a(a(x1))))))) = [0 0 1]x1 + [3] >= [0 0 1]x1 + [1] = a#(b(a(b(a(b(x1))))))
      
      a#(b(a(b(a(a(a(x1))))))) = [0 0 1]x1 + [3] >= [0 0 1]x1 + [1] = a#(b(a(b(x1))))
      
      a#(b(a(b(a(a(a(x1))))))) = [0 0 1]x1 + [3] >= [0 0 1]x1 + [1] = a#(b(x1))
      
                                [0 0 1]     [3]    [0 0 1]     [3]                                
      a(b(a(b(a(a(a(x1))))))) = [0 0 1]x1 + [3] >= [0 0 1]x1 + [3] = a(a(a(a(b(a(b(a(b(x1)))))))))
                                [0 0 1]     [2]    [0 0 1]     [2]                                
     problem:
      DPs:
       
      TRS:
       a(b(a(b(a(a(a(x1))))))) -> a(a(a(a(b(a(b(a(b(x1)))))))))
     Qed