[joshuamorton]

Probably not, the infinite loop rules are specifically about rules where a player cannot make a choice in the process.

It's possible that there's a way to do something turing-challenging or busy-beavery in such a situation, but it's usually pretty difficult to make complex unbendable loops, they're usually very direct cases where taking an action more or less forces you to immediately take the same action again, so the loop has...two steps. Anything much bigger or more complex and you're basically assured to have player choice.

There's probably room to do something where a player is clearly losing unless they do something which might continue a situation that is undecidable.

[tcbawo]

If you have two choices for spend/untap, I think it would be fairly trivial to create Turing complete logic that also presents discretion and requires involvement from the player. However, it sounds like such an arrangement can still considered a draw in “competitive play”. There are many formats to Magic, though. If any other Turing machine had an outside observer ready to pull the plug after an arbitrary amount of time, does it make it less of a Turing machine?

[themoonisachees]

Semantically, yes. Turing machines (actual ideal ones that only exist in maths papers) always compute forever. They are also instantaneous and have infinite resources.

The argument is that MtG is Turing complete except for that part, because it cannot compute forever, even in an ideal scenario where time and space are infinitely available, because the rules explicitly forbid it.

An ideal Turing machine with someone to pull the plug is not a Turing machine. Also: just because humans can recognize some infinite loops doesn't mean we can recognize all infinite loops, so the person pulling the plug may be misinterpreting and pulling the plug on a machine that would otherwise eventually halt.