YES

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

Proof:
 DP Processor:
  DPs:
   a#(a(a(x1))) -> b#(x1)
   a#(a(a(x1))) -> a#(b(x1))
   a#(a(a(x1))) -> a#(a(b(x1)))
   b#(a(b(x1))) -> a#(x1)
   b#(a(b(x1))) -> b#(a(x1))
   b#(a(b(x1))) -> a#(b(a(x1)))
  TRS:
   a(a(a(x1))) -> a(a(b(x1)))
   b(a(b(x1))) -> a(b(a(x1)))
  TDG Processor:
   DPs:
    a#(a(a(x1))) -> b#(x1)
    a#(a(a(x1))) -> a#(b(x1))
    a#(a(a(x1))) -> a#(a(b(x1)))
    b#(a(b(x1))) -> a#(x1)
    b#(a(b(x1))) -> b#(a(x1))
    b#(a(b(x1))) -> a#(b(a(x1)))
   TRS:
    a(a(a(x1))) -> a(a(b(x1)))
    b(a(b(x1))) -> a(b(a(x1)))
   graph:
    b#(a(b(x1))) -> b#(a(x1)) -> b#(a(b(x1))) -> a#(b(a(x1)))
    b#(a(b(x1))) -> b#(a(x1)) -> b#(a(b(x1))) -> b#(a(x1))
    b#(a(b(x1))) -> b#(a(x1)) -> b#(a(b(x1))) -> a#(x1)
    b#(a(b(x1))) -> a#(b(a(x1))) -> a#(a(a(x1))) -> a#(a(b(x1)))
    b#(a(b(x1))) -> a#(b(a(x1))) -> a#(a(a(x1))) -> a#(b(x1))
    b#(a(b(x1))) -> a#(b(a(x1))) -> a#(a(a(x1))) -> b#(x1)
    b#(a(b(x1))) -> a#(x1) -> a#(a(a(x1))) -> a#(a(b(x1)))
    b#(a(b(x1))) -> a#(x1) -> a#(a(a(x1))) -> a#(b(x1))
    b#(a(b(x1))) -> a#(x1) -> a#(a(a(x1))) -> b#(x1)
    a#(a(a(x1))) -> b#(x1) -> b#(a(b(x1))) -> a#(b(a(x1)))
    a#(a(a(x1))) -> b#(x1) -> b#(a(b(x1))) -> b#(a(x1))
    a#(a(a(x1))) -> b#(x1) -> b#(a(b(x1))) -> a#(x1)
    a#(a(a(x1))) -> a#(b(x1)) -> a#(a(a(x1))) -> a#(a(b(x1)))
    a#(a(a(x1))) -> a#(b(x1)) -> a#(a(a(x1))) -> a#(b(x1))
    a#(a(a(x1))) -> a#(b(x1)) -> a#(a(a(x1))) -> b#(x1)
    a#(a(a(x1))) -> a#(a(b(x1))) -> a#(a(a(x1))) -> a#(a(b(x1)))
    a#(a(a(x1))) -> a#(a(b(x1))) -> a#(a(a(x1))) -> a#(b(x1))
    a#(a(a(x1))) -> a#(a(b(x1))) -> a#(a(a(x1))) -> b#(x1)
   Arctic Interpretation Processor:
    dimension: 1
    interpretation:
     [b#](x0) = 1x0,
     
     [a#](x0) = x0,
     
     [b](x0) = 2x0,
     
     [a](x0) = 2x0
    orientation:
     a#(a(a(x1))) = 4x1 >= 1x1 = b#(x1)
     
     a#(a(a(x1))) = 4x1 >= 2x1 = a#(b(x1))
     
     a#(a(a(x1))) = 4x1 >= 4x1 = a#(a(b(x1)))
     
     b#(a(b(x1))) = 5x1 >= x1 = a#(x1)
     
     b#(a(b(x1))) = 5x1 >= 3x1 = b#(a(x1))
     
     b#(a(b(x1))) = 5x1 >= 4x1 = a#(b(a(x1)))
     
     a(a(a(x1))) = 6x1 >= 6x1 = a(a(b(x1)))
     
     b(a(b(x1))) = 6x1 >= 6x1 = a(b(a(x1)))
    problem:
     DPs:
      a#(a(a(x1))) -> a#(a(b(x1)))
     TRS:
      a(a(a(x1))) -> a(a(b(x1)))
      b(a(b(x1))) -> a(b(a(x1)))
    EDG Processor:
     DPs:
      a#(a(a(x1))) -> a#(a(b(x1)))
     TRS:
      a(a(a(x1))) -> a(a(b(x1)))
      b(a(b(x1))) -> a(b(a(x1)))
     graph:
      a#(a(a(x1))) -> a#(a(b(x1))) -> a#(a(a(x1))) -> a#(a(b(x1)))
     Arctic Interpretation Processor:
      dimension: 3
      interpretation:
       [a#](x0) = [1 0 0]x0 + [0],
       
                 [-& 0  -&]     [0]
       [b](x0) = [-& 0  -&]x0 + [0]
                 [-& 0  1 ]     [1],
       
                 [1  1  -&]     [1]
       [a](x0) = [-& -& 0 ]x0 + [0]
                 [-& -& -&]     [0]
      orientation:
       a#(a(a(x1))) = [3 3 2]x1 + [3] >= [-& 2  1 ]x1 + [2] = a#(a(b(x1)))
       
                     [3  3  2 ]     [3]    [-& 2  2 ]     [2]              
       a(a(a(x1))) = [-& -& -&]x1 + [0] >= [-& -& -&]x1 + [0] = a(a(b(x1)))
                     [-& -& -&]     [0]    [-& -& -&]     [0]              
       
                     [-& 0  1 ]     [1]    [-& -& 1 ]     [1]              
       b(a(b(x1))) = [-& 0  1 ]x1 + [1] >= [-& -& 0 ]x1 + [1] = a(b(a(x1)))
                     [-& 0  1 ]     [1]    [-& -& -&]     [0]              
      problem:
       DPs:
        
       TRS:
        a(a(a(x1))) -> a(a(b(x1)))
        b(a(b(x1))) -> a(b(a(x1)))
      Qed