YES

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

Proof:
 DP Processor:
  DPs:
   a#(a(a(b(x1)))) -> a#(x1)
   a#(a(a(b(x1)))) -> a#(a(x1))
   a#(a(a(b(x1)))) -> a#(a(a(x1)))
   a#(a(a(b(x1)))) -> a#(b(a(a(a(x1)))))
  TRS:
   a(a(a(b(x1)))) -> b(a(b(a(a(a(x1))))))
   a(b(x1)) -> x1
  EDG Processor:
   DPs:
    a#(a(a(b(x1)))) -> a#(x1)
    a#(a(a(b(x1)))) -> a#(a(x1))
    a#(a(a(b(x1)))) -> a#(a(a(x1)))
    a#(a(a(b(x1)))) -> a#(b(a(a(a(x1)))))
   TRS:
    a(a(a(b(x1)))) -> b(a(b(a(a(a(x1))))))
    a(b(x1)) -> x1
   graph:
    a#(a(a(b(x1)))) -> a#(a(a(x1))) -> a#(a(a(b(x1)))) -> a#(x1)
    a#(a(a(b(x1)))) -> a#(a(a(x1))) -> a#(a(a(b(x1)))) -> a#(a(x1))
    a#(a(a(b(x1)))) -> a#(a(a(x1))) ->
    a#(a(a(b(x1)))) -> a#(a(a(x1)))
    a#(a(a(b(x1)))) -> a#(a(a(x1))) ->
    a#(a(a(b(x1)))) -> a#(b(a(a(a(x1)))))
    a#(a(a(b(x1)))) -> a#(a(x1)) -> a#(a(a(b(x1)))) -> a#(x1)
    a#(a(a(b(x1)))) -> a#(a(x1)) -> a#(a(a(b(x1)))) -> a#(a(x1))
    a#(a(a(b(x1)))) -> a#(a(x1)) -> a#(a(a(b(x1)))) -> a#(a(a(x1)))
    a#(a(a(b(x1)))) -> a#(a(x1)) -> a#(a(a(b(x1)))) -> a#(b(a(a(a(x1)))))
    a#(a(a(b(x1)))) -> a#(x1) -> a#(a(a(b(x1)))) -> a#(x1)
    a#(a(a(b(x1)))) -> a#(x1) -> a#(a(a(b(x1)))) -> a#(a(x1))
    a#(a(a(b(x1)))) -> a#(x1) -> a#(a(a(b(x1)))) -> a#(a(a(x1)))
    a#(a(a(b(x1)))) -> a#(x1) -> a#(a(a(b(x1)))) -> a#(b(a(a(a(x1)))))
   SCC Processor:
    #sccs: 1
    #rules: 3
    #arcs: 12/16
    DPs:
     a#(a(a(b(x1)))) -> a#(a(a(x1)))
     a#(a(a(b(x1)))) -> a#(a(x1))
     a#(a(a(b(x1)))) -> a#(x1)
    TRS:
     a(a(a(b(x1)))) -> b(a(b(a(a(a(x1))))))
     a(b(x1)) -> x1
    Arctic Interpretation Processor:
     dimension: 4
     interpretation:
      [a#](x0) = [0 0 0 0]x0 + [0],
      
                [-& 1  0  0 ]     [0 ]
                [-& 0  0  -&]     [-&]
      [a](x0) = [0  0  0  0 ]x0 + [0 ]
                [0  0  0  0 ]     [0 ],
      
                [0  0  0  0 ]     [0 ]
                [-& -& -& -&]     [-&]
      [b](x0) = [0  0  0  0 ]x0 + [0 ]
                [0  0  -& 0 ]     [0 ]
     orientation:
      a#(a(a(b(x1)))) = [1 1 1 1]x1 + [1] >= [0 1 1 0]x1 + [0] = a#(a(a(x1)))
      
      a#(a(a(b(x1)))) = [1 1 1 1]x1 + [1] >= [0 1 0 0]x1 + [0] = a#(a(x1))
      
      a#(a(a(b(x1)))) = [1 1 1 1]x1 + [1] >= [0 0 0 0]x1 + [0] = a#(x1)
      
                       [1 1 1 1]     [1]    [1  1  1  1 ]     [1 ]                       
                       [0 0 0 0]     [0]    [-& -& -& -&]     [-&]                       
      a(a(a(b(x1)))) = [1 1 1 1]x1 + [1] >= [1  1  1  1 ]x1 + [1 ] = b(a(b(a(a(a(x1))))))
                       [1 1 1 1]     [1]    [1  1  1  1 ]     [1 ]                       
      
                 [0 0 0 0]     [0]           
                 [0 0 0 0]     [0]           
      a(b(x1)) = [0 0 0 0]x1 + [0] >= x1 = x1
                 [0 0 0 0]     [0]           
     problem:
      DPs:
       a#(a(a(b(x1)))) -> a#(a(a(x1)))
       a#(a(a(b(x1)))) -> a#(a(x1))
      TRS:
       a(a(a(b(x1)))) -> b(a(b(a(a(a(x1))))))
       a(b(x1)) -> x1
     EDG Processor:
      DPs:
       a#(a(a(b(x1)))) -> a#(a(a(x1)))
       a#(a(a(b(x1)))) -> a#(a(x1))
      TRS:
       a(a(a(b(x1)))) -> b(a(b(a(a(a(x1))))))
       a(b(x1)) -> x1
      graph:
       a#(a(a(b(x1)))) -> a#(a(a(x1))) ->
       a#(a(a(b(x1)))) -> a#(a(a(x1)))
       a#(a(a(b(x1)))) -> a#(a(a(x1))) -> a#(a(a(b(x1)))) -> a#(a(x1))
       a#(a(a(b(x1)))) -> a#(a(x1)) -> a#(a(a(b(x1)))) -> a#(a(a(x1)))
       a#(a(a(b(x1)))) -> a#(a(x1)) -> a#(a(a(b(x1)))) -> a#(a(x1))
      Arctic Interpretation Processor:
       dimension: 4
       interpretation:
        [a#](x0) = [-& -& -& 0 ]x0 + [0],
        
                  [0  0  0  0 ]     [-&]
                  [-& -& 0  -&]     [0 ]
        [a](x0) = [-& -& -& 0 ]x0 + [0 ]
                  [-& 0  -& -&]     [0 ],
        
                  [0  0  0  1 ]     [0]
                  [-& -& 0  0 ]     [0]
        [b](x0) = [-& 0  1  0 ]x0 + [1]
                  [-& -& 0  -&]     [0]
       orientation:
        a#(a(a(b(x1)))) = [-& 0  1  0 ]x1 + [1] >= [-& -& 0  -&]x1 + [0] = a#(a(a(x1)))
        
        a#(a(a(b(x1)))) = [-& 0  1  0 ]x1 + [1] >= [-& 0  -& -&]x1 + [0] = a#(a(x1))
        
                         [0  0  1  1 ]     [1]    [0  0  1  1 ]     [1]                       
                         [-& -& 0  0 ]     [0]    [-& -& 0  0 ]     [0]                       
        a(a(a(b(x1)))) = [-& 0  1  0 ]x1 + [1] >= [-& 0  1  0 ]x1 + [1] = b(a(b(a(a(a(x1))))))
                         [-& -& 0  -&]     [0]    [-& -& 0  -&]     [0]                       
        
                   [0  0  1  1 ]     [1]           
                   [-& 0  1  0 ]     [1]           
        a(b(x1)) = [-& -& 0  -&]x1 + [0] >= x1 = x1
                   [-& -& 0  0 ]     [0]           
       problem:
        DPs:
         a#(a(a(b(x1)))) -> a#(a(x1))
        TRS:
         a(a(a(b(x1)))) -> b(a(b(a(a(a(x1))))))
         a(b(x1)) -> x1
       EDG Processor:
        DPs:
         a#(a(a(b(x1)))) -> a#(a(x1))
        TRS:
         a(a(a(b(x1)))) -> b(a(b(a(a(a(x1))))))
         a(b(x1)) -> x1
        graph:
         a#(a(a(b(x1)))) -> a#(a(x1)) -> a#(a(a(b(x1)))) -> a#(a(x1))
        CDG Processor:
         DPs:
          a#(a(a(b(x1)))) -> a#(a(x1))
         TRS:
          a(a(a(b(x1)))) -> b(a(b(a(a(a(x1))))))
          a(b(x1)) -> x1
         graph:
          
         Qed