YES

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

Proof:
 DP Processor:
  DPs:
   b#(a(b(x1))) -> a#(x1)
   a#(a(a(x1))) -> b#(x1)
   b#(b(x1)) -> a#(b(x1))
   b#(b(x1)) -> b#(a(b(x1)))
  TRS:
   b(a(b(x1))) -> a(x1)
   a(a(a(x1))) -> b(x1)
   b(b(x1)) -> b(a(b(x1)))
  TDG Processor:
   DPs:
    b#(a(b(x1))) -> a#(x1)
    a#(a(a(x1))) -> b#(x1)
    b#(b(x1)) -> a#(b(x1))
    b#(b(x1)) -> b#(a(b(x1)))
   TRS:
    b(a(b(x1))) -> a(x1)
    a(a(a(x1))) -> b(x1)
    b(b(x1)) -> b(a(b(x1)))
   graph:
    a#(a(a(x1))) -> b#(x1) -> b#(b(x1)) -> b#(a(b(x1)))
    a#(a(a(x1))) -> b#(x1) -> b#(b(x1)) -> a#(b(x1))
    a#(a(a(x1))) -> b#(x1) -> b#(a(b(x1))) -> a#(x1)
    b#(a(b(x1))) -> a#(x1) -> a#(a(a(x1))) -> b#(x1)
    b#(b(x1)) -> a#(b(x1)) -> a#(a(a(x1))) -> b#(x1)
    b#(b(x1)) -> b#(a(b(x1))) -> b#(b(x1)) -> b#(a(b(x1)))
    b#(b(x1)) -> b#(a(b(x1))) -> b#(b(x1)) -> a#(b(x1))
    b#(b(x1)) -> b#(a(b(x1))) -> b#(a(b(x1))) -> a#(x1)
   Arctic Interpretation Processor:
    dimension: 2
    interpretation:
     [a#](x0) = [0 0]x0 + [1],
     
     [b#](x0) = [0  -&]x0 + [2],
     
               [-& 0 ]     [1 ]
     [a](x0) = [3  0 ]x0 + [-&],
     
               [3 0]     [1]
     [b](x0) = [3 0]x0 + [0]
    orientation:
     b#(a(b(x1))) = [3 0]x1 + [2] >= [0 0]x1 + [1] = a#(x1)
     
     a#(a(a(x1))) = [3 3]x1 + [4] >= [0  -&]x1 + [2] = b#(x1)
     
     b#(b(x1)) = [3 0]x1 + [2] >= [3 0]x1 + [1] = a#(b(x1))
     
     b#(b(x1)) = [3 0]x1 + [2] >= [3 0]x1 + [2] = b#(a(b(x1)))
     
                   [6 3]     [4]    [-& 0 ]     [1 ]        
     b(a(b(x1))) = [6 3]x1 + [4] >= [3  0 ]x1 + [-&] = a(x1)
     
                   [3 3]     [4]    [3 0]     [1]        
     a(a(a(x1))) = [6 3]x1 + [4] >= [3 0]x1 + [0] = b(x1)
     
                [6 3]     [4]    [6 3]     [4]              
     b(b(x1)) = [6 3]x1 + [4] >= [6 3]x1 + [4] = b(a(b(x1)))
    problem:
     DPs:
      b#(a(b(x1))) -> a#(x1)
      b#(b(x1)) -> a#(b(x1))
      b#(b(x1)) -> b#(a(b(x1)))
     TRS:
      b(a(b(x1))) -> a(x1)
      a(a(a(x1))) -> b(x1)
      b(b(x1)) -> b(a(b(x1)))
    EDG Processor:
     DPs:
      b#(a(b(x1))) -> a#(x1)
      b#(b(x1)) -> a#(b(x1))
      b#(b(x1)) -> b#(a(b(x1)))
     TRS:
      b(a(b(x1))) -> a(x1)
      a(a(a(x1))) -> b(x1)
      b(b(x1)) -> b(a(b(x1)))
     graph:
      b#(b(x1)) -> b#(a(b(x1))) -> b#(a(b(x1))) -> a#(x1)
      b#(b(x1)) -> b#(a(b(x1))) -> b#(b(x1)) -> a#(b(x1))
      b#(b(x1)) -> b#(a(b(x1))) -> b#(b(x1)) -> b#(a(b(x1)))
     SCC Processor:
      #sccs: 1
      #rules: 1
      #arcs: 3/9
      DPs:
       b#(b(x1)) -> b#(a(b(x1)))
      TRS:
       b(a(b(x1))) -> a(x1)
       a(a(a(x1))) -> b(x1)
       b(b(x1)) -> b(a(b(x1)))
      Arctic Interpretation Processor:
       dimension: 2
       interpretation:
        [b#](x0) = [3 1]x0 + [0],
        
                  [-& 1 ]     [0]
        [a](x0) = [0  2 ]x0 + [1],
        
                  [3 2]     [2]
        [b](x0) = [0 0]x0 + [0]
       orientation:
        b#(b(x1)) = [6 5]x1 + [5] >= [4 4]x1 + [4] = b#(a(b(x1)))
        
                      [5 4]     [4]    [-& 1 ]     [0]        
        b(a(b(x1))) = [3 2]x1 + [2] >= [0  2 ]x1 + [1] = a(x1)
        
                      [3 5]     [4]    [3 2]     [2]        
        a(a(a(x1))) = [4 6]x1 + [5] >= [0 0]x1 + [0] = b(x1)
        
                   [6 5]     [5]    [5 4]     [4]              
        b(b(x1)) = [3 2]x1 + [2] >= [3 2]x1 + [2] = b(a(b(x1)))
       problem:
        DPs:
         
        TRS:
         b(a(b(x1))) -> a(x1)
         a(a(a(x1))) -> b(x1)
         b(b(x1)) -> b(a(b(x1)))
       Qed