Physics/Engineering question (Composite sync to Vertical/Horizontal sync)

I remember learning some equations about capacitors in school but I've long since forgotten this stuff and now I find that it would actually be useful for solving the below problem.

Here is how the game, Star Rider, derives vertical and horizontal sync by getting a composite sync input.  My question is, how?  How can one solve this on paper and predict when vsync and hsync will go low by only knowing the timing to csync and the resistance and capacitor values of this circuit?

The timing to csync (composite sync) is shown here (item 'b'):

Csync will either be 5V or ground.

Here is the circuit used in Star Rider:

W3 is connected, W4 is unconnected.  All of the NOT gates are a 74LS14.