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:
     [b#](x0) = [-& 0 ]x0 + [0],
     
     [a#](x0) = [0 0]x0,
     
               [0 0]     [0]
     [a](x0) = [0 0]x0 + [0],
     
               [0 1]     [0 ]
     [b](x0) = [0 0]x0 + [-&]
    orientation:
     a#(a(b(x1))) = [0 1]x1 + [0] >= [0 0]x1 = a#(x1)
     
     a#(b(a(x1))) = [1 1]x1 + [1] >= [0 0]x1 + [0] = b#(b(a(x1)))
     
     b#(b(x1)) = [0 0]x1 + [0] >= [0 0]x1 = a#(x1)
     
     b#(b(x1)) = [0 0]x1 + [0] >= [0 0]x1 + [0] = a#(a(x1))
     
     b#(b(x1)) = [0 0]x1 + [0] >= [0 0]x1 + [0] = a#(a(a(x1)))
     
                   [0 1]     [0]    [0 0]     [0]        
     a(a(b(x1))) = [0 1]x1 + [0] >= [0 0]x1 + [0] = a(x1)
     
                   [1 1]     [1]    [1 1]     [1]              
     a(b(a(x1))) = [1 1]x1 + [1] >= [1 1]x1 + [1] = b(b(a(x1)))
     
                [1 1]     [0]    [0 0]     [0]              
     b(b(x1)) = [0 1]x1 + [0] >= [0 0]x1 + [0] = a(a(a(x1)))
    problem:
     DPs:
      a#(a(b(x1))) -> 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)))
    Restore Modifier:
     DPs:
      a#(a(b(x1))) -> 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)))
     EDG Processor:
      DPs:
       a#(a(b(x1))) -> 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#(a(b(x1))) -> a#(x1)
       b#(b(x1)) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(x1)
       b#(b(x1)) -> 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#(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: 2/16