YES

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

Proof:
 DP Processor:
  DPs:
   b#(a(x1)) -> b#(x1)
   b#(a(x1)) -> a#(b(x1))
   a#(a(a(x1))) -> b#(x1)
   a#(a(a(x1))) -> a#(b(x1))
   a#(a(a(x1))) -> a#(a(b(x1)))
   a#(a(a(x1))) -> b#(a(a(b(x1))))
   b#(b(b(b(x1)))) -> a#(x1)
  TRS:
   b(a(x1)) -> a(b(x1))
   a(a(a(x1))) -> b(a(a(b(x1))))
   b(b(b(b(x1)))) -> a(x1)
  TDG Processor:
   DPs:
    b#(a(x1)) -> b#(x1)
    b#(a(x1)) -> a#(b(x1))
    a#(a(a(x1))) -> b#(x1)
    a#(a(a(x1))) -> a#(b(x1))
    a#(a(a(x1))) -> a#(a(b(x1)))
    a#(a(a(x1))) -> b#(a(a(b(x1))))
    b#(b(b(b(x1)))) -> a#(x1)
   TRS:
    b(a(x1)) -> a(b(x1))
    a(a(a(x1))) -> b(a(a(b(x1))))
    b(b(b(b(x1)))) -> a(x1)
   graph:
    a#(a(a(x1))) -> a#(b(x1)) -> a#(a(a(x1))) -> b#(a(a(b(x1))))
    a#(a(a(x1))) -> a#(b(x1)) -> a#(a(a(x1))) -> a#(a(b(x1)))
    a#(a(a(x1))) -> a#(b(x1)) -> a#(a(a(x1))) -> a#(b(x1))
    a#(a(a(x1))) -> a#(b(x1)) -> a#(a(a(x1))) -> b#(x1)
    a#(a(a(x1))) -> a#(a(b(x1))) -> a#(a(a(x1))) -> b#(a(a(b(x1))))
    a#(a(a(x1))) -> a#(a(b(x1))) -> a#(a(a(x1))) -> a#(a(b(x1)))
    a#(a(a(x1))) -> a#(a(b(x1))) -> a#(a(a(x1))) -> a#(b(x1))
    a#(a(a(x1))) -> a#(a(b(x1))) -> a#(a(a(x1))) -> b#(x1)
    a#(a(a(x1))) -> b#(a(a(b(x1)))) -> b#(b(b(b(x1)))) -> a#(x1)
    a#(a(a(x1))) -> b#(a(a(b(x1)))) -> b#(a(x1)) -> a#(b(x1))
    a#(a(a(x1))) -> b#(a(a(b(x1)))) -> b#(a(x1)) -> b#(x1)
    a#(a(a(x1))) -> b#(x1) -> b#(b(b(b(x1)))) -> a#(x1)
    a#(a(a(x1))) -> b#(x1) -> b#(a(x1)) -> a#(b(x1))
    a#(a(a(x1))) -> b#(x1) -> b#(a(x1)) -> b#(x1)
    b#(b(b(b(x1)))) -> a#(x1) -> a#(a(a(x1))) -> b#(a(a(b(x1))))
    b#(b(b(b(x1)))) -> a#(x1) -> a#(a(a(x1))) -> a#(a(b(x1)))
    b#(b(b(b(x1)))) -> a#(x1) -> a#(a(a(x1))) -> a#(b(x1))
    b#(b(b(b(x1)))) -> a#(x1) -> a#(a(a(x1))) -> b#(x1)
    b#(a(x1)) -> a#(b(x1)) -> a#(a(a(x1))) -> b#(a(a(b(x1))))
    b#(a(x1)) -> a#(b(x1)) -> a#(a(a(x1))) -> a#(a(b(x1)))
    b#(a(x1)) -> a#(b(x1)) -> a#(a(a(x1))) -> a#(b(x1))
    b#(a(x1)) -> a#(b(x1)) -> a#(a(a(x1))) -> b#(x1)
    b#(a(x1)) -> b#(x1) -> b#(b(b(b(x1)))) -> a#(x1)
    b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(b(x1))
    b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1)
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [a#](x0) = x0 + 12,
     
     [b#](x0) = x0 + 10,
     
     [b](x0) = x0 + 1,
     
     [a](x0) = x0 + 4
    orientation:
     b#(a(x1)) = x1 + 14 >= x1 + 10 = b#(x1)
     
     b#(a(x1)) = x1 + 14 >= x1 + 13 = a#(b(x1))
     
     a#(a(a(x1))) = x1 + 20 >= x1 + 10 = b#(x1)
     
     a#(a(a(x1))) = x1 + 20 >= x1 + 13 = a#(b(x1))
     
     a#(a(a(x1))) = x1 + 20 >= x1 + 17 = a#(a(b(x1)))
     
     a#(a(a(x1))) = x1 + 20 >= x1 + 19 = b#(a(a(b(x1))))
     
     b#(b(b(b(x1)))) = x1 + 13 >= x1 + 12 = a#(x1)
     
     b(a(x1)) = x1 + 5 >= x1 + 5 = a(b(x1))
     
     a(a(a(x1))) = x1 + 12 >= x1 + 10 = b(a(a(b(x1))))
     
     b(b(b(b(x1)))) = x1 + 4 >= x1 + 4 = a(x1)
    problem:
     DPs:
      
     TRS:
      b(a(x1)) -> a(b(x1))
      a(a(a(x1))) -> b(a(a(b(x1))))
      b(b(b(b(x1)))) -> a(x1)
    Qed