YES

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

Proof:
 DP Processor:
  DPs:
   b#(b(a(x1))) -> b#(x1)
   b#(b(a(x1))) -> b#(b(x1))
   b#(b(a(x1))) -> a#(b(b(x1)))
   b#(b(a(x1))) -> b#(a(b(b(x1))))
   b#(b(a(x1))) -> a#(b(a(b(b(x1)))))
  TRS:
   a(a(x1)) -> x1
   a(b(x1)) -> x1
   b(b(a(x1))) -> a(b(a(b(b(x1)))))
  TDG Processor:
   DPs:
    b#(b(a(x1))) -> b#(x1)
    b#(b(a(x1))) -> b#(b(x1))
    b#(b(a(x1))) -> a#(b(b(x1)))
    b#(b(a(x1))) -> b#(a(b(b(x1))))
    b#(b(a(x1))) -> a#(b(a(b(b(x1)))))
   TRS:
    a(a(x1)) -> x1
    a(b(x1)) -> x1
    b(b(a(x1))) -> a(b(a(b(b(x1)))))
   graph:
    b#(b(a(x1))) -> b#(b(x1)) -> b#(b(a(x1))) -> a#(b(a(b(b(x1)))))
    b#(b(a(x1))) -> b#(b(x1)) -> b#(b(a(x1))) -> b#(a(b(b(x1))))
    b#(b(a(x1))) -> b#(b(x1)) -> b#(b(a(x1))) -> a#(b(b(x1)))
    b#(b(a(x1))) -> b#(b(x1)) -> b#(b(a(x1))) -> b#(b(x1))
    b#(b(a(x1))) -> b#(b(x1)) -> b#(b(a(x1))) -> b#(x1)
    b#(b(a(x1))) -> b#(a(b(b(x1)))) ->
    b#(b(a(x1))) -> a#(b(a(b(b(x1)))))
    b#(b(a(x1))) -> b#(a(b(b(x1)))) ->
    b#(b(a(x1))) -> b#(a(b(b(x1))))
    b#(b(a(x1))) -> b#(a(b(b(x1)))) -> b#(b(a(x1))) -> a#(b(b(x1)))
    b#(b(a(x1))) -> b#(a(b(b(x1)))) -> b#(b(a(x1))) -> b#(b(x1))
    b#(b(a(x1))) -> b#(a(b(b(x1)))) -> b#(b(a(x1))) -> b#(x1)
    b#(b(a(x1))) -> b#(x1) -> b#(b(a(x1))) -> a#(b(a(b(b(x1)))))
    b#(b(a(x1))) -> b#(x1) -> b#(b(a(x1))) -> b#(a(b(b(x1))))
    b#(b(a(x1))) -> b#(x1) -> b#(b(a(x1))) -> a#(b(b(x1)))
    b#(b(a(x1))) -> b#(x1) -> b#(b(a(x1))) -> b#(b(x1))
    b#(b(a(x1))) -> b#(x1) -> b#(b(a(x1))) -> b#(x1)
   SCC Processor:
    #sccs: 1
    #rules: 3
    #arcs: 15/25
    DPs:
     b#(b(a(x1))) -> b#(b(x1))
     b#(b(a(x1))) -> b#(x1)
     b#(b(a(x1))) -> b#(a(b(b(x1))))
    TRS:
     a(a(x1)) -> x1
     a(b(x1)) -> x1
     b(b(a(x1))) -> a(b(a(b(b(x1)))))
    Arctic Interpretation Processor:
     dimension: 2
     usable rules:
      a(a(x1)) -> x1
      a(b(x1)) -> x1
      b(b(a(x1))) -> a(b(a(b(b(x1)))))
     interpretation:
      [b#](x0) = [0 2]x0 + [0],
      
                [-& 0 ]     [0]
      [b](x0) = [0  -&]x0 + [0],
      
                [2  0 ]     [3]
      [a](x0) = [0  -&]x0 + [1]
     orientation:
      b#(b(a(x1))) = [4 2]x1 + [5] >= [2 0]x1 + [2] = b#(b(x1))
      
      b#(b(a(x1))) = [4 2]x1 + [5] >= [0 2]x1 + [0] = b#(x1)
      
      b#(b(a(x1))) = [4 2]x1 + [5] >= [2 0]x1 + [3] = b#(a(b(b(x1))))
      
                 [4 2]     [5]           
      a(a(x1)) = [2 0]x1 + [3] >= x1 = x1
      
                 [0  2 ]     [3]           
      a(b(x1)) = [-& 0 ]x1 + [1] >= x1 = x1
      
                    [2  0 ]     [3]    [2  0 ]     [3]                    
      b(b(a(x1))) = [0  -&]x1 + [1] >= [0  -&]x1 + [1] = a(b(a(b(b(x1)))))
     problem:
      DPs:
       b#(b(a(x1))) -> b#(x1)
      TRS:
       a(a(x1)) -> x1
       a(b(x1)) -> x1
       b(b(a(x1))) -> a(b(a(b(b(x1)))))
     Restore Modifier:
      DPs:
       b#(b(a(x1))) -> b#(x1)
      TRS:
       a(a(x1)) -> x1
       a(b(x1)) -> x1
       b(b(a(x1))) -> a(b(a(b(b(x1)))))
      EDG Processor:
       DPs:
        b#(b(a(x1))) -> b#(x1)
       TRS:
        a(a(x1)) -> x1
        a(b(x1)) -> x1
        b(b(a(x1))) -> a(b(a(b(b(x1)))))
       graph:
        b#(b(a(x1))) -> b#(x1) -> b#(b(a(x1))) -> b#(x1)
       CDG Processor:
        DPs:
         b#(b(a(x1))) -> b#(x1)
        TRS:
         a(a(x1)) -> x1
         a(b(x1)) -> x1
         b(b(a(x1))) -> a(b(a(b(b(x1)))))
        graph:
         
        Qed