16 steps draw?
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I believe that it is 50.
50 moves.
FIDE laws of chess, Article 9.3. :
http://www.fide.com/component/handbook/?id=124&view=article
Ive looked at the game, and it seems that at some moments you were close to a 3-fold repetition draw. It may have occurred as well, but I didn't analyse it in details.
3-fold repetition is defined in Article 9.2. of Fide laws of chess.
Btw, your opponent obviously did not learn (properly) how to mate with 2 rooks. 