YES

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

Proof:
 DP Processor:
  DPs:
   a#(a(a(b(x1)))) -> a#(x1)
   a#(a(a(b(x1)))) -> b#(a(x1))
   a#(a(a(b(x1)))) -> a#(b(a(x1)))
   a#(a(a(b(x1)))) -> b#(a(b(a(x1))))
   b#(b(a(x1))) -> a#(b(a(x1)))
   b#(b(a(x1))) -> a#(a(b(a(x1))))
  TRS:
   a(a(a(b(x1)))) -> b(a(b(a(x1))))
   b(b(a(x1))) -> a(a(b(a(x1))))
  TDG Processor:
   DPs:
    a#(a(a(b(x1)))) -> a#(x1)
    a#(a(a(b(x1)))) -> b#(a(x1))
    a#(a(a(b(x1)))) -> a#(b(a(x1)))
    a#(a(a(b(x1)))) -> b#(a(b(a(x1))))
    b#(b(a(x1))) -> a#(b(a(x1)))
    b#(b(a(x1))) -> a#(a(b(a(x1))))
   TRS:
    a(a(a(b(x1)))) -> b(a(b(a(x1))))
    b(b(a(x1))) -> a(a(b(a(x1))))
   graph:
    b#(b(a(x1))) -> a#(a(b(a(x1)))) ->
    a#(a(a(b(x1)))) -> b#(a(b(a(x1))))
    b#(b(a(x1))) -> a#(a(b(a(x1)))) ->
    a#(a(a(b(x1)))) -> a#(b(a(x1)))
    b#(b(a(x1))) -> a#(a(b(a(x1)))) -> a#(a(a(b(x1)))) -> b#(a(x1))
    b#(b(a(x1))) -> a#(a(b(a(x1)))) -> a#(a(a(b(x1)))) -> a#(x1)
    b#(b(a(x1))) -> a#(b(a(x1))) -> a#(a(a(b(x1)))) -> b#(a(b(a(x1))))
    b#(b(a(x1))) -> a#(b(a(x1))) -> a#(a(a(b(x1)))) -> a#(b(a(x1)))
    b#(b(a(x1))) -> a#(b(a(x1))) -> a#(a(a(b(x1)))) -> b#(a(x1))
    b#(b(a(x1))) -> a#(b(a(x1))) -> a#(a(a(b(x1)))) -> a#(x1)
    a#(a(a(b(x1)))) -> b#(a(b(a(x1)))) ->
    b#(b(a(x1))) -> a#(a(b(a(x1))))
    a#(a(a(b(x1)))) -> b#(a(b(a(x1)))) -> b#(b(a(x1))) -> a#(b(a(x1)))
    a#(a(a(b(x1)))) -> b#(a(x1)) -> b#(b(a(x1))) -> a#(a(b(a(x1))))
    a#(a(a(b(x1)))) -> b#(a(x1)) -> b#(b(a(x1))) -> a#(b(a(x1)))
    a#(a(a(b(x1)))) -> a#(b(a(x1))) ->
    a#(a(a(b(x1)))) -> b#(a(b(a(x1))))
    a#(a(a(b(x1)))) -> a#(b(a(x1))) ->
    a#(a(a(b(x1)))) -> a#(b(a(x1)))
    a#(a(a(b(x1)))) -> a#(b(a(x1))) -> a#(a(a(b(x1)))) -> b#(a(x1))
    a#(a(a(b(x1)))) -> a#(b(a(x1))) -> a#(a(a(b(x1)))) -> a#(x1)
    a#(a(a(b(x1)))) -> a#(x1) -> a#(a(a(b(x1)))) -> b#(a(b(a(x1))))
    a#(a(a(b(x1)))) -> a#(x1) -> a#(a(a(b(x1)))) -> a#(b(a(x1)))
    a#(a(a(b(x1)))) -> a#(x1) -> a#(a(a(b(x1)))) -> b#(a(x1))
    a#(a(a(b(x1)))) -> a#(x1) -> a#(a(a(b(x1)))) -> a#(x1)
   Arctic Interpretation Processor:
    dimension: 4
    interpretation:
     [b#](x0) = [-& 0  -& -&]x0 + [0],
     
     [a#](x0) = [0  -& -& -&]x0,
     
               [0  -& -& 0 ]     [0 ]
               [0  -& -& -&]     [0 ]
     [a](x0) = [0  0  -& -&]x0 + [-&]
               [0  0  0  0 ]     [1 ],
     
               [-& 0  -& -&]     [0]
               [1  0  -& -&]     [0]
     [b](x0) = [0  0  -& -&]x0 + [1]
               [-& 0  -& -&]     [0]
    orientation:
     a#(a(a(b(x1)))) = [1  0  -& -&]x1 + [1] >= [0  -& -& -&]x1 = a#(x1)
     
     a#(a(a(b(x1)))) = [1  0  -& -&]x1 + [1] >= [0  -& -& -&]x1 + [0] = b#(a(x1))
     
     a#(a(a(b(x1)))) = [1  0  -& -&]x1 + [1] >= [0  -& -& -&]x1 + [0] = a#(b(a(x1)))
     
     a#(a(a(b(x1)))) = [1  0  -& -&]x1 + [1] >= [0  -& -& -&]x1 + [0] = b#(a(b(a(x1))))
     
     b#(b(a(x1))) = [1  -& -& 1 ]x1 + [1] >= [0  -& -& -&]x1 + [0] = a#(b(a(x1)))
     
     b#(b(a(x1))) = [1  -& -& 1 ]x1 + [1] >= [0  -& -& -&]x1 + [0] = a#(a(b(a(x1))))
     
                      [1  0  -& -&]     [1]    [0  -& -& -&]     [0]                 
                      [1  0  -& -&]     [1]    [1  -& -& -&]     [1]                 
     a(a(a(b(x1)))) = [1  0  -& -&]x1 + [1] >= [0  -& -& -&]x1 + [1] = b(a(b(a(x1))))
                      [1  0  -& -&]     [1]    [0  -& -& -&]     [0]                 
     
                   [1  -& -& 1 ]     [1]    [1  -& -& 1 ]     [1]                 
                   [1  -& -& 1 ]     [1]    [0  -& -& -&]     [0]                 
     b(b(a(x1))) = [1  -& -& 1 ]x1 + [1] >= [0  -& -& -&]x1 + [0] = a(a(b(a(x1))))
                   [1  -& -& 1 ]     [1]    [1  -& -& 1 ]     [1]                 
    problem:
     DPs:
      
     TRS:
      a(a(a(b(x1)))) -> b(a(b(a(x1))))
      b(b(a(x1))) -> a(a(b(a(x1))))
    Qed