YES

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

Proof:
 DP Processor:
  DPs:
   a#(a(b(x1))) -> a#(x1)
   a#(a(b(x1))) -> a#(a(x1))
   a#(a(b(x1))) -> b#(a(a(x1)))
   a#(a(b(x1))) -> a#(b(a(a(x1))))
   a#(a(b(x1))) -> b#(a(b(a(a(x1)))))
  TRS:
   a(x1) -> x1
   a(a(b(x1))) -> b(a(b(a(a(x1)))))
   b(b(x1)) -> b(x1)
  TDG Processor:
   DPs:
    a#(a(b(x1))) -> a#(x1)
    a#(a(b(x1))) -> a#(a(x1))
    a#(a(b(x1))) -> b#(a(a(x1)))
    a#(a(b(x1))) -> a#(b(a(a(x1))))
    a#(a(b(x1))) -> b#(a(b(a(a(x1)))))
   TRS:
    a(x1) -> x1
    a(a(b(x1))) -> b(a(b(a(a(x1)))))
    b(b(x1)) -> b(x1)
   graph:
    a#(a(b(x1))) -> a#(b(a(a(x1)))) ->
    a#(a(b(x1))) -> b#(a(b(a(a(x1)))))
    a#(a(b(x1))) -> a#(b(a(a(x1)))) ->
    a#(a(b(x1))) -> a#(b(a(a(x1))))
    a#(a(b(x1))) -> a#(b(a(a(x1)))) -> a#(a(b(x1))) -> b#(a(a(x1)))
    a#(a(b(x1))) -> a#(b(a(a(x1)))) -> a#(a(b(x1))) -> a#(a(x1))
    a#(a(b(x1))) -> a#(b(a(a(x1)))) -> a#(a(b(x1))) -> a#(x1)
    a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> b#(a(b(a(a(x1)))))
    a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(b(a(a(x1))))
    a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> b#(a(a(x1)))
    a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(a(x1))
    a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(x1)
    a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> b#(a(b(a(a(x1)))))
    a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(b(a(a(x1))))
    a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> b#(a(a(x1)))
    a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(a(x1))
    a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(x1)
   CDG Processor:
    DPs:
     a#(a(b(x1))) -> a#(x1)
     a#(a(b(x1))) -> a#(a(x1))
     a#(a(b(x1))) -> b#(a(a(x1)))
     a#(a(b(x1))) -> a#(b(a(a(x1))))
     a#(a(b(x1))) -> b#(a(b(a(a(x1)))))
    TRS:
     a(x1) -> x1
     a(a(b(x1))) -> b(a(b(a(a(x1)))))
     b(b(x1)) -> b(x1)
    graph:
     
    Qed