YES

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

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