YES

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

Proof:
 DP Processor:
  DPs:
   b#(a(a(x1))) -> b#(x1)
   b#(a(a(x1))) -> b#(a(b(x1)))
  TRS:
   b(b(x1)) -> a(a(a(x1)))
   b(a(b(x1))) -> a(x1)
   b(a(a(x1))) -> b(a(b(x1)))
  Arctic Interpretation Processor:
   dimension: 2
   interpretation:
    [b#](x0) = [1 1]x0 + [0],
    
              [-& 0 ]     [0]
    [a](x0) = [2  -&]x0 + [2],
    
              [-& 0 ]     [0]
    [b](x0) = [2  2 ]x0 + [2]
   orientation:
    b#(a(a(x1))) = [3 3]x1 + [3] >= [1 1]x1 + [0] = b#(x1)
    
    b#(a(a(x1))) = [3 3]x1 + [3] >= [3 3]x1 + [3] = b#(a(b(x1)))
    
               [2 2]     [2]    [-& 2 ]     [2]              
    b(b(x1)) = [4 4]x1 + [4] >= [4  -&]x1 + [4] = a(a(a(x1)))
    
                  [-& 2 ]     [2]    [-& 0 ]     [0]        
    b(a(b(x1))) = [4  4 ]x1 + [4] >= [2  -&]x1 + [2] = a(x1)
    
                  [-& 2 ]     [2]    [-& 2 ]     [2]              
    b(a(a(x1))) = [4  4 ]x1 + [4] >= [4  4 ]x1 + [4] = b(a(b(x1)))
   problem:
    DPs:
     b#(a(a(x1))) -> b#(a(b(x1)))
    TRS:
     b(b(x1)) -> a(a(a(x1)))
     b(a(b(x1))) -> a(x1)
     b(a(a(x1))) -> b(a(b(x1)))
   Arctic Interpretation Processor:
    dimension: 2
    interpretation:
     [b#](x0) = [0  -&]x0 + [0],
     
               [-& 0 ]     [0]
     [a](x0) = [2  -&]x0 + [1],
     
               [3  0 ]     [2 ]
     [b](x0) = [1  -&]x0 + [-&]
    orientation:
     b#(a(a(x1))) = [2  -&]x1 + [1] >= [1  -&]x1 + [0] = b#(a(b(x1)))
     
                [6 3]     [5]    [-& 2 ]     [2]              
     b(b(x1)) = [4 1]x1 + [3] >= [4  -&]x1 + [3] = a(a(a(x1)))
     
                   [5  2 ]     [4]    [-& 0 ]     [0]        
     b(a(b(x1))) = [2  -&]x1 + [1] >= [2  -&]x1 + [1] = a(x1)
     
                   [5  2 ]     [4]    [5  2 ]     [4]              
     b(a(a(x1))) = [3  -&]x1 + [2] >= [2  -&]x1 + [1] = b(a(b(x1)))
    problem:
     DPs:
      
     TRS:
      b(b(x1)) -> a(a(a(x1)))
      b(a(b(x1))) -> a(x1)
      b(a(a(x1))) -> b(a(b(x1)))
    Qed