NO

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

Proof:
 DP Processor:
  DPs:
   a#(a(a(a(x1)))) -> b#(a(a(a(x1))))
   b#(b(x1)) -> a#(b(x1))
   b#(b(x1)) -> a#(a(b(x1)))
  TRS:
   a(a(a(a(x1)))) -> b(a(a(a(x1))))
   b(b(x1)) -> a(a(b(x1)))
  TDG Processor:
   DPs:
    a#(a(a(a(x1)))) -> b#(a(a(a(x1))))
    b#(b(x1)) -> a#(b(x1))
    b#(b(x1)) -> a#(a(b(x1)))
   TRS:
    a(a(a(a(x1)))) -> b(a(a(a(x1))))
    b(b(x1)) -> a(a(b(x1)))
   graph:
    b#(b(x1)) -> a#(b(x1)) -> a#(a(a(a(x1)))) -> b#(a(a(a(x1))))
    b#(b(x1)) -> a#(a(b(x1))) ->
    a#(a(a(a(x1)))) -> b#(a(a(a(x1))))
    a#(a(a(a(x1)))) -> b#(a(a(a(x1)))) ->
    b#(b(x1)) -> a#(a(b(x1)))
    a#(a(a(a(x1)))) -> b#(a(a(a(x1)))) -> b#(b(x1)) -> a#(b(x1))
   Loop Processor:
    loop length: 9
    terms:
     b(b(b(a(a(a(a(a(a(b(x1))))))))))
     b(b(b(b(a(a(a(a(a(b(x1))))))))))
     b(a(a(b(b(a(a(a(a(a(b(x1)))))))))))
     b(a(a(b(b(b(a(a(a(a(b(x1)))))))))))
     b(a(a(a(a(b(b(a(a(a(a(b(x1))))))))))))
     b(a(a(a(a(a(a(b(a(a(a(a(b(x1)))))))))))))
     b(b(a(a(a(a(a(b(a(a(a(a(b(x1)))))))))))))
     b(b(a(a(a(a(a(b(b(a(a(a(b(x1)))))))))))))
     b(b(a(a(a(a(a(a(a(b(a(a(a(b(x1))))))))))))))
    context: []
    substitution:
     x1 -> a(a(a(b(x1))))
    Qed