Here’s a step-by-step approach, taking the rules one at a time:
Diagramming the 1st rule (L and Q each perform at some time after P):
Adding the 2nd rule (S performs at some time before O and L):
Adding the 3rd rule (M performs at some time before S):
Adding the 4th rule (P performs at some time after N):
Adding the 5th and final rule (S and N each perform at some time after R):
You may notice that my earlier version of the game’s final diagram had R a bit more to the bottom-left than I’ve depicted it above. Either way is fine. You have some flexibility with regard to exact appearance of the diagram.