YES

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

Proof:
 DP Processor:
  DPs:
   a#(b(b(a(x1)))) -> a#(b(b(x1)))
   a#(b(b(a(x1)))) -> a#(b(a(b(b(x1)))))
   a#(b(b(a(x1)))) -> a#(a(b(a(b(b(x1))))))
  TRS:
   a(a(x1)) -> x1
   a(b(b(a(x1)))) -> a(a(b(a(b(b(x1))))))
  Arctic Interpretation Processor:
   dimension: 2
   usable rules:
    a(a(x1)) -> x1
    a(b(b(a(x1)))) -> a(a(b(a(b(b(x1))))))
   interpretation:
    [a#](x0) = [-& 1 ]x0 + [0],
    
              [-& 0 ]     [0 ]
    [b](x0) = [0  -&]x0 + [-&],
    
              [-& 0 ]     [1]
    [a](x0) = [0  2 ]x0 + [3]
   orientation:
    a#(b(b(a(x1)))) = [1 3]x1 + [4] >= [-& 1 ]x1 + [1] = a#(b(b(x1)))
    
    a#(b(b(a(x1)))) = [1 3]x1 + [4] >= [-& 1 ]x1 + [2] = a#(b(a(b(b(x1)))))
    
    a#(b(b(a(x1)))) = [1 3]x1 + [4] >= [1 3]x1 + [4] = a#(a(b(a(b(b(x1))))))
    
               [0 2]     [3]           
    a(a(x1)) = [2 4]x1 + [5] >= x1 = x1
    
                     [0 2]     [3]    [0 2]     [3]                       
    a(b(b(a(x1)))) = [2 4]x1 + [5] >= [2 4]x1 + [5] = a(a(b(a(b(b(x1))))))
   problem:
    DPs:
     a#(b(b(a(x1)))) -> a#(a(b(a(b(b(x1))))))
    TRS:
     a(a(x1)) -> x1
     a(b(b(a(x1)))) -> a(a(b(a(b(b(x1))))))
   Restore Modifier:
    DPs:
     a#(b(b(a(x1)))) -> a#(a(b(a(b(b(x1))))))
    TRS:
     a(a(x1)) -> x1
     a(b(b(a(x1)))) -> a(a(b(a(b(b(x1))))))
    Arctic Interpretation Processor:
     dimension: 3
     usable rules:
      a(a(x1)) -> x1
      a(b(b(a(x1)))) -> a(a(b(a(b(b(x1))))))
     interpretation:
      [a#](x0) = [0  0  -&]x0 + [0],
      
                [-& -& 0 ]     [0 ]
      [b](x0) = [0  0  0 ]x0 + [-&]
                [0  -& -&]     [0 ],
      
                [-& -& 0 ]     [0]
      [a](x0) = [-& -& 0 ]x0 + [0]
                [0  0  1 ]     [1]
     orientation:
      a#(b(b(a(x1)))) = [0 0 1]x1 + [1] >= [-& -& 0 ]x1 + [0] = a#(a(b(a(b(b(x1))))))
      
                 [0 0 1]     [1]           
      a(a(x1)) = [0 0 1]x1 + [1] >= x1 = x1
                 [1 1 2]     [2]           
      
                       [0 0 1]     [1]    [0 0 1]     [1]                       
      a(b(b(a(x1)))) = [0 0 1]x1 + [1] >= [0 0 1]x1 + [1] = a(a(b(a(b(b(x1))))))
                       [1 1 2]     [2]    [1 1 2]     [2]                       
     problem:
      DPs:
       
      TRS:
       a(a(x1)) -> x1
       a(b(b(a(x1)))) -> a(a(b(a(b(b(x1))))))
     Qed