YES

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

Proof:
 DP Processor:
  DPs:
   a#(b(b(a(x1)))) -> b#(x1)
   a#(b(b(a(x1)))) -> a#(b(x1))
   a#(b(b(a(x1)))) -> a#(a(b(x1)))
   a#(b(b(a(x1)))) -> b#(a(a(b(x1))))
   b#(a(b(x1))) -> b#(b(x1))
   b#(a(b(x1))) -> b#(b(b(x1)))
   b#(a(b(x1))) -> a#(b(b(b(x1))))
  TRS:
   a(b(b(a(x1)))) -> b(a(a(b(x1))))
   b(a(b(x1))) -> a(b(b(b(x1))))
  TDG Processor:
   DPs:
    a#(b(b(a(x1)))) -> b#(x1)
    a#(b(b(a(x1)))) -> a#(b(x1))
    a#(b(b(a(x1)))) -> a#(a(b(x1)))
    a#(b(b(a(x1)))) -> b#(a(a(b(x1))))
    b#(a(b(x1))) -> b#(b(x1))
    b#(a(b(x1))) -> b#(b(b(x1)))
    b#(a(b(x1))) -> a#(b(b(b(x1))))
   TRS:
    a(b(b(a(x1)))) -> b(a(a(b(x1))))
    b(a(b(x1))) -> a(b(b(b(x1))))
   graph:
    b#(a(b(x1))) -> b#(b(b(x1))) -> b#(a(b(x1))) -> a#(b(b(b(x1))))
    b#(a(b(x1))) -> b#(b(b(x1))) -> b#(a(b(x1))) -> b#(b(b(x1)))
    b#(a(b(x1))) -> b#(b(b(x1))) -> b#(a(b(x1))) -> b#(b(x1))
    b#(a(b(x1))) -> b#(b(x1)) -> b#(a(b(x1))) -> a#(b(b(b(x1))))
    b#(a(b(x1))) -> b#(b(x1)) -> b#(a(b(x1))) -> b#(b(b(x1)))
    b#(a(b(x1))) -> b#(b(x1)) -> b#(a(b(x1))) -> b#(b(x1))
    b#(a(b(x1))) -> a#(b(b(b(x1)))) ->
    a#(b(b(a(x1)))) -> b#(a(a(b(x1))))
    b#(a(b(x1))) -> a#(b(b(b(x1)))) ->
    a#(b(b(a(x1)))) -> a#(a(b(x1)))
    b#(a(b(x1))) -> a#(b(b(b(x1)))) -> a#(b(b(a(x1)))) -> a#(b(x1))
    b#(a(b(x1))) -> a#(b(b(b(x1)))) -> a#(b(b(a(x1)))) -> b#(x1)
    a#(b(b(a(x1)))) -> b#(a(a(b(x1)))) ->
    b#(a(b(x1))) -> a#(b(b(b(x1))))
    a#(b(b(a(x1)))) -> b#(a(a(b(x1)))) ->
    b#(a(b(x1))) -> b#(b(b(x1)))
    a#(b(b(a(x1)))) -> b#(a(a(b(x1)))) -> b#(a(b(x1))) -> b#(b(x1))
    a#(b(b(a(x1)))) -> b#(x1) -> b#(a(b(x1))) -> a#(b(b(b(x1))))
    a#(b(b(a(x1)))) -> b#(x1) -> b#(a(b(x1))) -> b#(b(b(x1)))
    a#(b(b(a(x1)))) -> b#(x1) -> b#(a(b(x1))) -> b#(b(x1))
    a#(b(b(a(x1)))) -> a#(b(x1)) -> a#(b(b(a(x1)))) -> b#(a(a(b(x1))))
    a#(b(b(a(x1)))) -> a#(b(x1)) -> a#(b(b(a(x1)))) -> a#(a(b(x1)))
    a#(b(b(a(x1)))) -> a#(b(x1)) -> a#(b(b(a(x1)))) -> a#(b(x1))
    a#(b(b(a(x1)))) -> a#(b(x1)) -> a#(b(b(a(x1)))) -> b#(x1)
    a#(b(b(a(x1)))) -> a#(a(b(x1))) ->
    a#(b(b(a(x1)))) -> b#(a(a(b(x1))))
    a#(b(b(a(x1)))) -> a#(a(b(x1))) ->
    a#(b(b(a(x1)))) -> a#(a(b(x1)))
    a#(b(b(a(x1)))) -> a#(a(b(x1))) -> a#(b(b(a(x1)))) -> a#(b(x1))
    a#(b(b(a(x1)))) -> a#(a(b(x1))) -> a#(b(b(a(x1)))) -> b#(x1)
   Matrix Interpretation Processor: dim=3
    
    interpretation:
     [b#](x0) = [0 2 2]x0,
     
     [a#](x0) = [2 0 0]x0 + [1],
     
               [0 0 2]  
     [b](x0) = [0 1 0]x0
               [0 1 0]  ,
     
               [0 0 0]     [0]
     [a](x0) = [0 1 1]x0 + [1]
               [1 0 0]     [0]
    orientation:
     a#(b(b(a(x1)))) = [0 4 4]x1 + [5] >= [0 2 2]x1 = b#(x1)
     
     a#(b(b(a(x1)))) = [0 4 4]x1 + [5] >= [0 0 4]x1 + [1] = a#(b(x1))
     
     a#(b(b(a(x1)))) = [0 4 4]x1 + [5] >= [1] = a#(a(b(x1)))
     
     a#(b(b(a(x1)))) = [0 4 4]x1 + [5] >= [0 4 4]x1 + [4] = b#(a(a(b(x1))))
     
     b#(a(b(x1))) = [0 4 4]x1 + [2] >= [0 4 0]x1 = b#(b(x1))
     
     b#(a(b(x1))) = [0 4 4]x1 + [2] >= [0 4 0]x1 = b#(b(b(x1)))
     
     b#(a(b(x1))) = [0 4 4]x1 + [2] >= [0 4 0]x1 + [1] = a#(b(b(b(x1))))
     
                      [0 0 0]     [0]    [0 0 0]     [0]                 
     a(b(b(a(x1)))) = [0 2 2]x1 + [3] >= [0 2 2]x1 + [2] = b(a(a(b(x1))))
                      [0 2 2]     [2]    [0 2 2]     [2]                 
     
                   [0 0 4]     [0]    [0 0 0]     [0]                 
     b(a(b(x1))) = [0 2 0]x1 + [1] >= [0 2 0]x1 + [1] = a(b(b(b(x1))))
                   [0 2 0]     [1]    [0 2 0]     [0]                 
    problem:
     DPs:
      
     TRS:
      a(b(b(a(x1)))) -> b(a(a(b(x1))))
      b(a(b(x1))) -> a(b(b(b(x1))))
    Qed