A fun recent example mitigating the halting problem came from an affectionate troll level(o) in mario maker
I'm unsure whether the underlying implementation uses approximation techniques, as the op suggests, or if Nintendo simply identified potential halting offenders and added a layer of checks to overcome the intractable issue
note: the clip is loud and includes the player yelling fuck; in case that offends.. that said, the whole level playthrough is a lot of fun