YES

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

Proof:
 String Reversal Processor:
  b(a(a(a(x1)))) -> a(a(a(b(a(b(x1))))))
  a(b(x1)) -> x1
  DP Processor:
   DPs:
    b#(a(a(a(x1)))) -> b#(x1)
    b#(a(a(a(x1)))) -> a#(b(x1))
    b#(a(a(a(x1)))) -> b#(a(b(x1)))
    b#(a(a(a(x1)))) -> a#(b(a(b(x1))))
    b#(a(a(a(x1)))) -> a#(a(b(a(b(x1)))))
    b#(a(a(a(x1)))) -> a#(a(a(b(a(b(x1))))))
   TRS:
    b(a(a(a(x1)))) -> a(a(a(b(a(b(x1))))))
    a(b(x1)) -> x1
   TDG Processor:
    DPs:
     b#(a(a(a(x1)))) -> b#(x1)
     b#(a(a(a(x1)))) -> a#(b(x1))
     b#(a(a(a(x1)))) -> b#(a(b(x1)))
     b#(a(a(a(x1)))) -> a#(b(a(b(x1))))
     b#(a(a(a(x1)))) -> a#(a(b(a(b(x1)))))
     b#(a(a(a(x1)))) -> a#(a(a(b(a(b(x1))))))
    TRS:
     b(a(a(a(x1)))) -> a(a(a(b(a(b(x1))))))
     a(b(x1)) -> x1
    graph:
     b#(a(a(a(x1)))) -> b#(a(b(x1))) ->
     b#(a(a(a(x1)))) -> a#(a(a(b(a(b(x1))))))
     b#(a(a(a(x1)))) -> b#(a(b(x1))) ->
     b#(a(a(a(x1)))) -> a#(a(b(a(b(x1)))))
     b#(a(a(a(x1)))) -> b#(a(b(x1))) ->
     b#(a(a(a(x1)))) -> a#(b(a(b(x1))))
     b#(a(a(a(x1)))) -> b#(a(b(x1))) ->
     b#(a(a(a(x1)))) -> b#(a(b(x1)))
     b#(a(a(a(x1)))) -> b#(a(b(x1))) -> b#(a(a(a(x1)))) -> a#(b(x1))
     b#(a(a(a(x1)))) -> b#(a(b(x1))) -> b#(a(a(a(x1)))) -> b#(x1)
     b#(a(a(a(x1)))) -> b#(x1) -> b#(a(a(a(x1)))) -> a#(a(a(b(a(b(x1))))))
     b#(a(a(a(x1)))) -> b#(x1) -> b#(a(a(a(x1)))) -> a#(a(b(a(b(x1)))))
     b#(a(a(a(x1)))) -> b#(x1) -> b#(a(a(a(x1)))) -> a#(b(a(b(x1))))
     b#(a(a(a(x1)))) -> b#(x1) -> b#(a(a(a(x1)))) -> b#(a(b(x1)))
     b#(a(a(a(x1)))) -> b#(x1) -> b#(a(a(a(x1)))) -> a#(b(x1))
     b#(a(a(a(x1)))) -> b#(x1) -> b#(a(a(a(x1)))) -> b#(x1)
    SCC Processor:
     #sccs: 1
     #rules: 2
     #arcs: 12/36
     DPs:
      b#(a(a(a(x1)))) -> b#(a(b(x1)))
      b#(a(a(a(x1)))) -> b#(x1)
     TRS:
      b(a(a(a(x1)))) -> a(a(a(b(a(b(x1))))))
      a(b(x1)) -> x1
     Arctic Interpretation Processor:
      dimension: 4
      interpretation:
       [b#](x0) = [0  -& 0  0 ]x0 + [0],
       
                 [0  -& 0  -&]     [0]
                 [0  0  0  0 ]     [0]
       [a](x0) = [0  -& 0  0 ]x0 + [0]
                 [1  0  0  0 ]     [0],
       
                 [0  -& 0  -&]     [-&]
                 [0  0  0  0 ]     [0 ]
       [b](x0) = [0  -& 0  -&]x0 + [0 ]
                 [0  -& 0  -&]     [0 ]
      orientation:
       b#(a(a(a(x1)))) = [1 0 1 1]x1 + [1] >= [1 0 1 0]x1 + [0] = b#(a(b(x1)))
       
       b#(a(a(a(x1)))) = [1 0 1 1]x1 + [1] >= [0  -& 0  0 ]x1 + [0] = b#(x1)
       
                        [1 0 1 0]     [1]    [1 0 1 0]     [1]                       
                        [1 0 1 1]     [1]    [1 0 1 0]     [1]                       
       b(a(a(a(x1)))) = [1 0 1 0]x1 + [1] >= [1 0 1 0]x1 + [1] = a(a(a(b(a(b(x1))))))
                        [1 0 1 0]     [1]    [1 0 1 0]     [1]                       
       
                  [0  -& 0  -&]     [0]           
                  [0  0  0  0 ]     [0]           
       a(b(x1)) = [0  -& 0  -&]x1 + [0] >= x1 = x1
                  [1  0  1  0 ]     [0]           
      problem:
       DPs:
        b#(a(a(a(x1)))) -> b#(a(b(x1)))
       TRS:
        b(a(a(a(x1)))) -> a(a(a(b(a(b(x1))))))
        a(b(x1)) -> x1
      EDG Processor:
       DPs:
        b#(a(a(a(x1)))) -> b#(a(b(x1)))
       TRS:
        b(a(a(a(x1)))) -> a(a(a(b(a(b(x1))))))
        a(b(x1)) -> x1
       graph:
        b#(a(a(a(x1)))) -> b#(a(b(x1))) -> b#(a(a(a(x1)))) -> b#(a(b(x1)))
       Arctic Interpretation Processor:
        dimension: 3
        interpretation:
         [b#](x0) = [-& -& 0 ]x0 + [0],
         
                   [-& 1  0 ]     [0]
         [a](x0) = [-& -& 0 ]x0 + [1]
                   [0  0  -&]     [0],
         
                   [-& -& 0 ]     [0]
         [b](x0) = [-& -& 0 ]x0 + [0]
                   [0  0  1 ]     [0]
        orientation:
         b#(a(a(a(x1)))) = [0 0 1]x1 + [2] >= [-& -& 0 ]x1 + [0] = b#(a(b(x1)))
         
                          [0 0 1]     [2]    [0 0 1]     [2]                       
         b(a(a(a(x1)))) = [0 0 1]x1 + [2] >= [0 0 1]x1 + [1] = a(a(a(b(a(b(x1))))))
                          [1 1 2]     [3]    [1 1 2]     [2]                       
         
                    [0  0  1 ]     [1]           
         a(b(x1)) = [0  0  1 ]x1 + [1] >= x1 = x1
                    [-& -& 0 ]     [0]           
        problem:
         DPs:
          
         TRS:
          b(a(a(a(x1)))) -> a(a(a(b(a(b(x1))))))
          a(b(x1)) -> x1
        Qed