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: 3
    interpretation:
     [b#](x0) = [-& 0  -&]x0 + [1],
     
     [a#](x0) = [-& -& 0 ]x0 + [0],
     
               [0  0  0 ]     [1]
     [a](x0) = [-& -& 0 ]x0 + [0]
               [0  -& -&]     [0],
     
               [-& 0  -&]     [0]
     [b](x0) = [-& 0  1 ]x0 + [0]
               [-& 0  -&]     [0]
    orientation:
     a#(a(a(b(x1)))) = [-& 0  1 ]x1 + [1] >= [-& -& 0 ]x1 + [0] = a#(x1)
     
     a#(a(a(b(x1)))) = [-& 0  1 ]x1 + [1] >= [-& -& 0 ]x1 + [1] = b#(a(x1))
     
     a#(a(a(b(x1)))) = [-& 0  1 ]x1 + [1] >= [-& -& 0 ]x1 + [0] = a#(b(a(x1)))
     
     a#(a(a(b(x1)))) = [-& 0  1 ]x1 + [1] >= [-& -& 0 ]x1 + [1] = b#(a(b(a(x1))))
     
     b#(b(a(x1))) = [1  -& 0 ]x1 + [1] >= [-& -& 0 ]x1 + [0] = a#(b(a(x1)))
     
     b#(b(a(x1))) = [1  -& 0 ]x1 + [1] >= [-& -& 0 ]x1 + [0] = a#(a(b(a(x1))))
     
                      [-& 0  1 ]     [1]    [-& -& 0 ]     [0]                 
     a(a(a(b(x1)))) = [-& 0  1 ]x1 + [1] >= [-& -& 1 ]x1 + [1] = b(a(b(a(x1))))
                      [-& 0  1 ]     [1]    [-& -& 0 ]     [0]                 
     
                   [1  -& 0 ]     [1]    [1  -& 0 ]     [1]                 
     b(b(a(x1))) = [1  -& 1 ]x1 + [1] >= [-& -& 0 ]x1 + [0] = a(a(b(a(x1))))
                   [1  -& 0 ]     [1]    [1  -& 0 ]     [1]                 
    problem:
     DPs:
      a#(a(a(b(x1)))) -> 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))))
    EDG Processor:
     DPs:
      a#(a(a(b(x1)))) -> 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(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#(b(a(x1))) ->
      a#(a(a(b(x1)))) -> b#(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(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)))) -> b#(a(x1)) -> b#(b(a(x1))) -> a#(a(b(a(x1))))
     Arctic Interpretation Processor:
      dimension: 3
      interpretation:
       [b#](x0) = [1  -& -&]x0 + [0],
       
       [a#](x0) = [-& 0  0 ]x0 + [0],
       
                 [-& 0  -&]     [0]
       [a](x0) = [-& -& 0 ]x0 + [0]
                 [0  0  0 ]     [0],
       
                 [0  1  -&]     [1 ]
       [b](x0) = [0  -& -&]x0 + [0 ]
                 [0  -& -&]     [-&]
      orientation:
       a#(a(a(b(x1)))) = [0  1  -&]x1 + [1] >= [-& 1  -&]x1 + [1] = b#(a(x1))
       
       a#(a(a(b(x1)))) = [0  1  -&]x1 + [1] >= [-& 1  -&]x1 + [1] = b#(a(b(a(x1))))
       
       b#(b(a(x1))) = [-& 1  2 ]x1 + [2] >= [-& 0  -&]x1 + [0] = a#(b(a(x1)))
       
       b#(b(a(x1))) = [-& 1  2 ]x1 + [2] >= [-& 0  1 ]x1 + [1] = a#(a(b(a(x1))))
       
                        [0  1  -&]     [1]    [-& 1  -&]     [1]                 
       a(a(a(b(x1)))) = [0  1  -&]x1 + [1] >= [-& 0  -&]x1 + [0] = b(a(b(a(x1))))
                        [0  1  -&]     [1]    [-& 0  -&]     [0]                 
       
                     [-& 1  1 ]     [1]    [-& 0  -&]     [0]                 
       b(b(a(x1))) = [-& 0  1 ]x1 + [1] >= [-& 0  1 ]x1 + [1] = a(a(b(a(x1))))
                     [-& 0  1 ]     [1]    [-& 0  1 ]     [1]                 
      problem:
       DPs:
        a#(a(a(b(x1)))) -> b#(a(x1))
        a#(a(a(b(x1)))) -> b#(a(b(a(x1))))
       TRS:
        a(a(a(b(x1)))) -> b(a(b(a(x1))))
        b(b(a(x1))) -> a(a(b(a(x1))))
      EDG Processor:
       DPs:
        a#(a(a(b(x1)))) -> b#(a(x1))
        a#(a(a(b(x1)))) -> b#(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:
        
       Qed