YES

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

Proof:
 DP Processor:
  DPs:
   a#(a(b(x1))) -> a#(x1)
   a#(b(a(x1))) -> b#(b(a(x1)))
   b#(b(x1)) -> a#(x1)
   b#(b(x1)) -> a#(a(x1))
   b#(b(x1)) -> a#(a(a(x1)))
  TRS:
   a(a(b(x1))) -> a(x1)
   a(b(a(x1))) -> b(b(a(x1)))
   b(b(x1)) -> a(a(a(x1)))
  TDG Processor:
   DPs:
    a#(a(b(x1))) -> a#(x1)
    a#(b(a(x1))) -> b#(b(a(x1)))
    b#(b(x1)) -> a#(x1)
    b#(b(x1)) -> a#(a(x1))
    b#(b(x1)) -> a#(a(a(x1)))
   TRS:
    a(a(b(x1))) -> a(x1)
    a(b(a(x1))) -> b(b(a(x1)))
    b(b(x1)) -> a(a(a(x1)))
   graph:
    b#(b(x1)) -> a#(a(a(x1))) -> a#(b(a(x1))) -> b#(b(a(x1)))
    b#(b(x1)) -> a#(a(a(x1))) -> a#(a(b(x1))) -> a#(x1)
    b#(b(x1)) -> a#(a(x1)) -> a#(b(a(x1))) -> b#(b(a(x1)))
    b#(b(x1)) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(x1)
    b#(b(x1)) -> a#(x1) -> a#(b(a(x1))) -> b#(b(a(x1)))
    b#(b(x1)) -> a#(x1) -> a#(a(b(x1))) -> a#(x1)
    a#(a(b(x1))) -> a#(x1) -> a#(b(a(x1))) -> b#(b(a(x1)))
    a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(x1)
    a#(b(a(x1))) -> b#(b(a(x1))) -> b#(b(x1)) -> a#(a(a(x1)))
    a#(b(a(x1))) -> b#(b(a(x1))) -> b#(b(x1)) -> a#(a(x1))
    a#(b(a(x1))) -> b#(b(a(x1))) -> b#(b(x1)) -> a#(x1)
   Arctic Interpretation Processor:
    dimension: 2
    usable rules:
     a(a(b(x1))) -> a(x1)
     a(b(a(x1))) -> b(b(a(x1)))
     b(b(x1)) -> a(a(a(x1)))
    interpretation:
               [0 0]  
     [a](x0) = [0 0]x0,
     
     [b#](x0) = [-& 3 ]x0 + [1],
     
               [-& 1 ]     [2 ]
     [b](x0) = [0  0 ]x0 + [-&],
     
     [a#](x0) = [2 0]x0 + [0]
    orientation:
     a#(a(b(x1))) = [2 3]x1 + [4] >= [2 0]x1 + [0] = a#(x1)
     
     a#(b(a(x1))) = [3 3]x1 + [4] >= [3 3]x1 + [1] = b#(b(a(x1)))
     
     b#(b(x1)) = [3 3]x1 + [1] >= [2 0]x1 + [0] = a#(x1)
     
     b#(b(x1)) = [3 3]x1 + [1] >= [2 2]x1 + [0] = a#(a(x1))
     
     b#(b(x1)) = [3 3]x1 + [1] >= [2 2]x1 + [0] = a#(a(a(x1)))
     
                   [0 1]     [2]    [0 0]          
     a(a(b(x1))) = [0 1]x1 + [2] >= [0 0]x1 = a(x1)
     
                   [1 1]     [2]    [1 1]     [2]              
     a(b(a(x1))) = [1 1]x1 + [2] >= [1 1]x1 + [2] = b(b(a(x1)))
     
                [1 1]     [2]    [0 0]                
     b(b(x1)) = [0 1]x1 + [2] >= [0 0]x1 = a(a(a(x1)))
    problem:
     DPs:
      a#(a(b(x1))) -> a#(x1)
      a#(b(a(x1))) -> b#(b(a(x1)))
     TRS:
      a(a(b(x1))) -> a(x1)
      a(b(a(x1))) -> b(b(a(x1)))
      b(b(x1)) -> a(a(a(x1)))
    Restore Modifier:
     DPs:
      a#(a(b(x1))) -> a#(x1)
      a#(b(a(x1))) -> b#(b(a(x1)))
     TRS:
      a(a(b(x1))) -> a(x1)
      a(b(a(x1))) -> b(b(a(x1)))
      b(b(x1)) -> a(a(a(x1)))
     EDG Processor:
      DPs:
       a#(a(b(x1))) -> a#(x1)
       a#(b(a(x1))) -> b#(b(a(x1)))
      TRS:
       a(a(b(x1))) -> a(x1)
       a(b(a(x1))) -> b(b(a(x1)))
       b(b(x1)) -> a(a(a(x1)))
      graph:
       a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(x1)
       a#(a(b(x1))) -> a#(x1) -> a#(b(a(x1))) -> b#(b(a(x1)))
      SCC Processor:
       #sccs: 1
       #rules: 1
       #arcs: 2/4
       DPs:
        a#(a(b(x1))) -> a#(x1)
       TRS:
        a(a(b(x1))) -> a(x1)
        a(b(a(x1))) -> b(b(a(x1)))
        b(b(x1)) -> a(a(a(x1)))
       Usable Rule Processor:
        DPs:
         a#(a(b(x1))) -> a#(x1)
        TRS:
         
        Arctic Interpretation Processor:
         dimension: 1
         usable rules:
          
         interpretation:
          [a](x0) = x0 + 0,
          
          [b](x0) = 1x0 + 13,
          
          [a#](x0) = x0
         orientation:
          a#(a(b(x1))) = 1x1 + 13 >= x1 = a#(x1)
         problem:
          DPs:
           
          TRS:
           
         Qed