YES

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

Proof:
 DP Processor:
  DPs:
   a#(b(b(x1))) -> a#(x1)
   a#(a(x1)) -> b#(x1)
   a#(a(x1)) -> b#(b(x1))
   a#(a(x1)) -> b#(b(b(x1)))
   b#(b(a(x1))) -> a#(b(a(x1)))
  TRS:
   a(b(b(x1))) -> a(x1)
   a(a(x1)) -> b(b(b(x1)))
   b(b(a(x1))) -> a(b(a(x1)))
  TDG Processor:
   DPs:
    a#(b(b(x1))) -> a#(x1)
    a#(a(x1)) -> b#(x1)
    a#(a(x1)) -> b#(b(x1))
    a#(a(x1)) -> b#(b(b(x1)))
    b#(b(a(x1))) -> a#(b(a(x1)))
   TRS:
    a(b(b(x1))) -> a(x1)
    a(a(x1)) -> b(b(b(x1)))
    b(b(a(x1))) -> a(b(a(x1)))
   graph:
    b#(b(a(x1))) -> a#(b(a(x1))) -> a#(a(x1)) -> b#(b(b(x1)))
    b#(b(a(x1))) -> a#(b(a(x1))) -> a#(a(x1)) -> b#(b(x1))
    b#(b(a(x1))) -> a#(b(a(x1))) -> a#(a(x1)) -> b#(x1)
    b#(b(a(x1))) -> a#(b(a(x1))) -> a#(b(b(x1))) -> a#(x1)
    a#(a(x1)) -> b#(b(b(x1))) -> b#(b(a(x1))) -> a#(b(a(x1)))
    a#(a(x1)) -> b#(b(x1)) -> b#(b(a(x1))) -> a#(b(a(x1)))
    a#(a(x1)) -> b#(x1) -> b#(b(a(x1))) -> a#(b(a(x1)))
    a#(b(b(x1))) -> a#(x1) -> a#(a(x1)) -> b#(b(b(x1)))
    a#(b(b(x1))) -> a#(x1) -> a#(a(x1)) -> b#(b(x1))
    a#(b(b(x1))) -> a#(x1) -> a#(a(x1)) -> b#(x1)
    a#(b(b(x1))) -> a#(x1) -> a#(b(b(x1))) -> a#(x1)
   Arctic Interpretation Processor:
    dimension: 2
    interpretation:
     [b#](x0) = [-1 -3]x0 + [0],
     
     [a#](x0) = [-& 3 ]x0 + [0],
     
               [-4 1 ]     [0]
     [a](x0) = [-2 3 ]x0 + [3],
     
               [-& 2 ]     [2]
     [b](x0) = [-1 -&]x0 + [0]
    orientation:
     a#(b(b(x1))) = [-& 4 ]x1 + [4] >= [-& 3 ]x1 + [0] = a#(x1)
     
     a#(a(x1)) = [1 6]x1 + [6] >= [-1 -3]x1 + [0] = b#(x1)
     
     a#(a(x1)) = [1 6]x1 + [6] >= [-4 1 ]x1 + [1] = b#(b(x1))
     
     a#(a(x1)) = [1 6]x1 + [6] >= [0  -2]x1 + [1] = b#(b(b(x1)))
     
     b#(b(a(x1))) = [-1 4 ]x1 + [4] >= [-2 3 ]x1 + [3] = a#(b(a(x1)))
     
                   [-3 2 ]     [2]    [-4 1 ]     [0]        
     a(b(b(x1))) = [-1 4 ]x1 + [4] >= [-2 3 ]x1 + [3] = a(x1)
     
                [-1 4 ]     [4]    [-& 3 ]     [3]              
     a(a(x1)) = [1  6 ]x1 + [6] >= [0  -&]x1 + [1] = b(b(b(x1)))
     
                   [-3 2 ]     [2]    [-4 1 ]     [1]              
     b(b(a(x1))) = [-1 4 ]x1 + [4] >= [-2 3 ]x1 + [3] = a(b(a(x1)))
    problem:
     DPs:
      
     TRS:
      a(b(b(x1))) -> a(x1)
      a(a(x1)) -> b(b(b(x1)))
      b(b(a(x1))) -> a(b(a(x1)))
    Qed