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:
                [-& 0 ]     [0]
      [b](x0) = [0  -&]x0 + [1],
      
      [b#](x0) = [0  -&]x0 + [0],
      
                [-& 0 ]     [0]
      [a](x0) = [0  1 ]x0 + [3]
     orientation:
      b#(b(a(x1))) = [0 1]x1 + [3] >= [-& 0 ]x1 + [0] = b#(b(x1))
      
      b#(b(a(x1))) = [0 1]x1 + [3] >= [0  -&]x1 + [0] = b#(x1)
      
      b#(b(a(x1))) = [0 1]x1 + [3] >= [-& 0 ]x1 + [1] = b#(a(b(b(x1))))
      
                 [0 1]     [3]           
      a(a(x1)) = [1 2]x1 + [4] >= x1 = x1
      
                 [0  -&]     [1]           
      a(b(x1)) = [1  0 ]x1 + [3] >= x1 = x1
      
                    [-& 0 ]     [1]    [-& 0 ]     [1]                    
      b(b(a(x1))) = [0  1 ]x1 + [3] >= [0  1 ]x1 + [3] = 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)
       Usable Rule Processor:
        DPs:
         b#(b(a(x1))) -> b#(x1)
        TRS:
         
        Arctic Interpretation Processor:
         dimension: 1
         usable rules:
          
         interpretation:
          [b](x0) = x0 + 0,
          
          [b#](x0) = x0,
          
          [a](x0) = 1x0 + 13
         orientation:
          b#(b(a(x1))) = 1x1 + 13 >= x1 = b#(x1)
         problem:
          DPs:
           
          TRS:
           
         Qed