If you haven't seen this chart you might find it helpful. Keep in mind that these are just estimates/averages, and that the times of REM and non-REM are going to vary for everyone and depend on your own physiology as well as your lifestyle. The key is just to find what works for you through experimentation by waking up at different times. I prefer to WILD after only 3.5 hours, because then I feel like I have the rest of my sleep to spend lucid dreaming, which gives me at least an hour or so of LDs. Where as other people prefer to try WILDing after something more like 6 hours of sleep, since the REM cycles are longer and it is easier to get lucid. But really, I'd suggest to think less about the exact timing, because it's probably going to vary, so you can't really say...in 20 minutes you'll be in REM, because in theory that might be correct, but that doesn't mean it's definitely going to happen.