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
    interpretation:
     [b#](x0) = [2 0]x0 + [3],
     
     [a#](x0) = [0 3]x0 + [0],
     
               [0  2 ]     [3]
     [a](x0) = [-& 0 ]x0 + [0],
     
               [-& 2 ]     [0]
     [b](x0) = [1  0 ]x0 + [2]
    orientation:
     a#(a(b(x1))) = [4 3]x1 + [5] >= [0 3]x1 + [0] = a#(x1)
     
     a#(b(a(x1))) = [4 6]x1 + [7] >= [1 4]x1 + [4] = b#(b(a(x1)))
     
     b#(b(x1)) = [1 4]x1 + [3] >= [0 3]x1 + [0] = a#(x1)
     
     b#(b(x1)) = [1 4]x1 + [3] >= [0 3]x1 + [3] = a#(a(x1))
     
     b#(b(x1)) = [1 4]x1 + [3] >= [0 3]x1 + [3] = a#(a(a(x1)))
     
                   [3 2]     [4]    [0  2 ]     [3]        
     a(a(b(x1))) = [1 0]x1 + [2] >= [-& 0 ]x1 + [0] = a(x1)
     
                   [3 5]     [6]    [3 5]     [6]              
     a(b(a(x1))) = [1 3]x1 + [4] >= [1 3]x1 + [4] = b(b(a(x1)))
     
                [3 2]     [4]    [0  2 ]     [3]              
     b(b(x1)) = [1 3]x1 + [2] >= [-& 0 ]x1 + [0] = a(a(a(x1)))
    problem:
     DPs:
      a#(a(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)))
    EDG Processor:
     DPs:
      a#(a(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#(a(b(x1))) -> a#(x1)
      b#(b(x1)) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(x1)
      a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(x1)
     CDG Processor:
      DPs:
       a#(a(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#(a(b(x1))) -> a#(x1)
       b#(b(x1)) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(x1)
      SCC Processor:
       #sccs: 0
       #rules: 0
       #arcs: 2/9