So ASoS will be covered by Seasons 3 and 4 (2013-14). AFFC/ADWD will likely be covered by Season 5-6 (2015-16). So TWoW will need to come out in 2016 so the producers have enough lead time to work on it.

This is - just about - doable. GRRM said in a recent interview he'd managed to get back to TWoW but not to a huge degree so far. As of next month, he'll have written maybe 2-3 new chapters for TWoW in a year, which is not great progress (though his PR duties for ADWD and the HBO series have been significant). He's really only got 3-3.5 years to finish TWoW in time for it to come out in 2016. The good news is that he was chomping to get back to it, as he was in the middle of laying out the three big battles the book starts with and apparently it was going well.

However, Weiss and Benioff have said they envisage the series as likely topping out at 80 episodes ( 8 seasons), maybe 90 at the absolute maximum. Given that GRRM envisages Books 6 and 7 as being the same size as ASOS/ADWD, that could potentially mean they require multiple seasons each. The only way to make that work will be for Books 6-7 to span three seasons (Seasons 7-9). And that means A DREAM OF SPRING will need to be ready by the middle of 2017.

Which is not going to happen. Certainly unless GRRM drops every other project and cancels most of his public appearances for the next five years, which I doubt very much will happen. And of course it absolutely requires the books not to expand to eight volumes, which is more likely than not at this stage.

At this point, I consider it almost inevitable we will see the end of A SONG OF ICE AND FIRE on screen before - potentially years before - we read it in print.