YES

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

Proof:
 DP Processor:
  DPs:
   a#(a(b(x1))) -> a#(x1)
   a#(a(b(x1))) -> a#(a(x1))
   a#(a(b(x1))) -> b#(a(a(x1)))
   a#(a(b(x1))) -> a#(b(a(a(x1))))
   a#(a(b(x1))) -> b#(a(b(a(a(x1)))))
  TRS:
   a(a(x1)) -> x1
   a(a(b(x1))) -> b(a(b(a(a(x1)))))
   b(b(x1)) -> x1
  TDG Processor:
   DPs:
    a#(a(b(x1))) -> a#(x1)
    a#(a(b(x1))) -> a#(a(x1))
    a#(a(b(x1))) -> b#(a(a(x1)))
    a#(a(b(x1))) -> a#(b(a(a(x1))))
    a#(a(b(x1))) -> b#(a(b(a(a(x1)))))
   TRS:
    a(a(x1)) -> x1
    a(a(b(x1))) -> b(a(b(a(a(x1)))))
    b(b(x1)) -> x1
   graph:
    a#(a(b(x1))) -> a#(b(a(a(x1)))) ->
    a#(a(b(x1))) -> b#(a(b(a(a(x1)))))
    a#(a(b(x1))) -> a#(b(a(a(x1)))) ->
    a#(a(b(x1))) -> a#(b(a(a(x1))))
    a#(a(b(x1))) -> a#(b(a(a(x1)))) -> a#(a(b(x1))) -> b#(a(a(x1)))
    a#(a(b(x1))) -> a#(b(a(a(x1)))) -> a#(a(b(x1))) -> a#(a(x1))
    a#(a(b(x1))) -> a#(b(a(a(x1)))) -> a#(a(b(x1))) -> a#(x1)
    a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> b#(a(b(a(a(x1)))))
    a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(b(a(a(x1))))
    a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> b#(a(a(x1)))
    a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(a(x1))
    a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(x1)
    a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> b#(a(b(a(a(x1)))))
    a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(b(a(a(x1))))
    a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> b#(a(a(x1)))
    a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(a(x1))
    a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(x1)
   SCC Processor:
    #sccs: 1
    #rules: 3
    #arcs: 15/25
    DPs:
     a#(a(b(x1))) -> a#(b(a(a(x1))))
     a#(a(b(x1))) -> a#(x1)
     a#(a(b(x1))) -> a#(a(x1))
    TRS:
     a(a(x1)) -> x1
     a(a(b(x1))) -> b(a(b(a(a(x1)))))
     b(b(x1)) -> x1
    Arctic Interpretation Processor:
     dimension: 2
     usable rules:
      a(a(x1)) -> x1
      a(a(b(x1))) -> b(a(b(a(a(x1)))))
      b(b(x1)) -> x1
     interpretation:
      [a#](x0) = [-& 0 ]x0 + [0],
      
                [1  0 ]     [3]
      [b](x0) = [0  -&]x0 + [2],
      
                [-& 0 ]     [0]
      [a](x0) = [0  -&]x0 + [0]
     orientation:
      a#(a(b(x1))) = [1 0]x1 + [3] >= [0  -&]x1 + [2] = a#(b(a(a(x1))))
      
      a#(a(b(x1))) = [1 0]x1 + [3] >= [-& 0 ]x1 + [0] = a#(x1)
      
      a#(a(b(x1))) = [1 0]x1 + [3] >= [0  -&]x1 + [0] = a#(a(x1))
      
                      [0]           
      a(a(x1)) = x1 + [0] >= x1 = x1
      
                    [1  0 ]     [3]    [1  0 ]     [3]                    
      a(a(b(x1))) = [0  -&]x1 + [2] >= [0  -&]x1 + [2] = b(a(b(a(a(x1)))))
      
                 [2 1]     [4]           
      b(b(x1)) = [1 0]x1 + [3] >= x1 = x1
     problem:
      DPs:
       a#(a(b(x1))) -> a#(x1)
      TRS:
       a(a(x1)) -> x1
       a(a(b(x1))) -> b(a(b(a(a(x1)))))
       b(b(x1)) -> x1
     Restore Modifier:
      DPs:
       a#(a(b(x1))) -> a#(x1)
      TRS:
       a(a(x1)) -> x1
       a(a(b(x1))) -> b(a(b(a(a(x1)))))
       b(b(x1)) -> x1
      EDG Processor:
       DPs:
        a#(a(b(x1))) -> a#(x1)
       TRS:
        a(a(x1)) -> x1
        a(a(b(x1))) -> b(a(b(a(a(x1)))))
        b(b(x1)) -> x1
       graph:
        a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(x1)
       CDG Processor:
        DPs:
         a#(a(b(x1))) -> a#(x1)
        TRS:
         a(a(x1)) -> x1
         a(a(b(x1))) -> b(a(b(a(a(x1)))))
         b(b(x1)) -> x1
        graph:
         
        Qed