YES

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

Proof:
 DP Processor:
  DPs:
   b#(a(b(a(b(b(x1)))))) -> b#(a(x1))
   b#(a(b(a(b(b(x1)))))) -> b#(b(a(x1)))
   b#(a(b(a(b(b(x1)))))) -> b#(b(b(a(x1))))
   b#(a(b(a(b(b(x1)))))) -> b#(a(b(b(b(a(x1))))))
  TRS:
   b(a(b(a(b(b(x1)))))) -> a(b(a(b(b(b(a(x1)))))))
  CDG Processor:
   DPs:
    b#(a(b(a(b(b(x1)))))) -> b#(a(x1))
    b#(a(b(a(b(b(x1)))))) -> b#(b(a(x1)))
    b#(a(b(a(b(b(x1)))))) -> b#(b(b(a(x1))))
    b#(a(b(a(b(b(x1)))))) -> b#(a(b(b(b(a(x1))))))
   TRS:
    b(a(b(a(b(b(x1)))))) -> a(b(a(b(b(b(a(x1)))))))
   graph:
    b#(a(b(a(b(b(x1)))))) -> b#(a(x1)) ->
    b#(a(b(a(b(b(x1)))))) -> b#(a(x1))
    b#(a(b(a(b(b(x1)))))) -> b#(a(x1)) ->
    b#(a(b(a(b(b(x1)))))) -> b#(b(a(x1)))
    b#(a(b(a(b(b(x1)))))) -> b#(a(x1)) ->
    b#(a(b(a(b(b(x1)))))) -> b#(b(b(a(x1))))
    b#(a(b(a(b(b(x1)))))) -> b#(a(x1)) ->
    b#(a(b(a(b(b(x1)))))) -> b#(a(b(b(b(a(x1))))))
    b#(a(b(a(b(b(x1)))))) -> b#(b(a(x1))) ->
    b#(a(b(a(b(b(x1)))))) -> b#(a(x1))
    b#(a(b(a(b(b(x1)))))) -> b#(b(a(x1))) ->
    b#(a(b(a(b(b(x1)))))) -> b#(b(a(x1)))
    b#(a(b(a(b(b(x1)))))) -> b#(b(a(x1))) ->
    b#(a(b(a(b(b(x1)))))) -> b#(b(b(a(x1))))
    b#(a(b(a(b(b(x1)))))) -> b#(b(a(x1))) ->
    b#(a(b(a(b(b(x1)))))) -> b#(a(b(b(b(a(x1))))))
    b#(a(b(a(b(b(x1)))))) -> b#(b(b(a(x1)))) ->
    b#(a(b(a(b(b(x1)))))) -> b#(a(x1))
    b#(a(b(a(b(b(x1)))))) -> b#(b(b(a(x1)))) ->
    b#(a(b(a(b(b(x1)))))) -> b#(b(a(x1)))
    b#(a(b(a(b(b(x1)))))) -> b#(b(b(a(x1)))) ->
    b#(a(b(a(b(b(x1)))))) -> b#(b(b(a(x1))))
    b#(a(b(a(b(b(x1)))))) -> b#(b(b(a(x1)))) -> b#(a(b(a(b(b(x1)))))) -> b#(a(b(b(b(a(x1))))))
   SCC Processor:
    #sccs: 1
    #rules: 3
    #arcs: 12/16
    DPs:
     b#(a(b(a(b(b(x1)))))) -> b#(a(x1))
     b#(a(b(a(b(b(x1)))))) -> b#(b(b(a(x1))))
     b#(a(b(a(b(b(x1)))))) -> b#(b(a(x1)))
    TRS:
     b(a(b(a(b(b(x1)))))) -> a(b(a(b(b(b(a(x1)))))))
    Arctic Interpretation Processor:
     dimension: 1
     interpretation:
      [b#](x0) = x0,
      
      [a](x0) = x0,
      
      [b](x0) = 4x0
     orientation:
      b#(a(b(a(b(b(x1)))))) = 12x1 >= x1 = b#(a(x1))
      
      b#(a(b(a(b(b(x1)))))) = 12x1 >= 8x1 = b#(b(b(a(x1))))
      
      b#(a(b(a(b(b(x1)))))) = 12x1 >= 4x1 = b#(b(a(x1)))
      
      b(a(b(a(b(b(x1)))))) = 16x1 >= 16x1 = a(b(a(b(b(b(a(x1)))))))
     problem:
      DPs:
       
      TRS:
       b(a(b(a(b(b(x1)))))) -> a(b(a(b(b(b(a(x1)))))))
     Qed