The halting problem's undecidability prevents you from writing a program that is guaranteed to prove whether other arbitrary programs halt or not. You can't write a halting-checker program and then feed it the source code to your AGI and have it say "this halts" or "this doesn't halt".
You can prove that some specific programs halt. If you're trying to prove it about a program that you are writing at the time, it can even be easy. I have written many programs that halt on all input sequences, and then proved this fact about them.
Here's a super-easy example: print "hello world" provably always halts.
"Since you play the game to get gold and experience points, making the game easier will let you get more gold per unit time: the game will become more fun."
I know this statement is being set up to be knocked down but when I read it I recoiled in disgust. Many people already do not play games with the end goal of increasing the values in the computer that represent gold or experience, because that is a completely empty and pointless thing to care about. My goal when playing games is "to improve myself" and has been for several years. The most fun I have when playing a game is just after I improve my own skill enough to overcome some challenge in a game that I couldn't do before.
I mainly play competitive multiplayer games and extremely difficult singleplayer games. I refuse to play any multiplayer game with meaningful persistent character state because that inevitably makes the game revolve around grinding. Grinding is pointless and stupid and typically does not develop much skill.
"For me at least, for something to be fun, I have to know that there's a challenge. For it to be a challenge, there has to be the possibility of failure."
I go farther than this. For a game to be significantly fun for me I have to ACTUALLY FAIL. Repeatedly. Until I get good.