Because that will fail to detect a program that halts in X+1 time. The problem isn’t to detect if a program that halts halts, the problem is to generally create an algorithm that will guarantee that the analyzed program will always halt given an infinite time running on an infinite computer.

Check out programming.dev for a Comp Sci focused community.

Exactly in the same boat. I would pick up this game in a second on PC, but with all the GamePass, free Epic, and Steam sale games I have there is zero need to ever get a PS5.