I have played P&P RPGs which are not simple at all but the combat still flows fast because all the info needed for it is right there condensed on the players character sheets. All in one place. After a couple of combat turns the player already knows all there is to know about his attack and damage and just needs to roll the dice. The thing that takes longer is when there is a player that is very indecisive and doesn't know if it should attack or do something else...
Another way of making the combat faster is to roll all the dice at once. In D&D you roll the d20 to hit and then the weapon damage dice for damage. If you roll the d20 and the damage dice all at once you save some time, in a big battle that shaves off several precious minutes
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That's what I feel as well... In my opinion PnP systems have to be really simple with only the most essential rules, like Fate, and focus on storytelling or they have to be fleshed out and focus on detail. Nothing in between... There is no good compromise between the two I think.
If you have a problem with slow combat it can be a problem of the system, but as Risewild pointed out, it is much more often the players that slow everything down, especially because of lack of knowledge of the rules. If, as the GM, I ever have to look anything up for one of my players, especially when it is a rule that only affects that one player because it is about his weapon etc. I tell him to learn his own f***ing rules or he will not apply them next time.
Unfortunately in many groups there is the idea that the GM has to know and process everything and the player can lean back and be entertained. But that is absolutely not how it works. When my D&D players don't know the rules, they won't use them and they will lose. I don't care! I will use all the combat rules to my NPC's advantage... ^_^
No ruleset is so extensive that 4 to 5 people can't learn and use it fluidly. But if you still have to look up rules all the time, it is probably because the rules are made like this.
Any system with a lot of tables for example! Hate that! Throw it in the fire! ^_^
Rules can be detailed and even complex, but the general mechanics have to be somewhat generic so they apply to most rolls and things have to have an inner logic so you can easily adapt rules to any situation or easily remember rules because they are only variations of that logic.
As for Retrocaplypse, it has some nice ideas and some interesting approaches, but I wouldn't wanna play it ... it lacks too much substance for my taste.