system
Given the following post, respond as if you're commenting on Reddit:
human
Does time travel into the past imply the Halting Problem is decidable?

Rule: Assume that there are unbounded resources including time.

&#x200B;

If the message will be sent by ourselves, we will receive the YES **instantly.** If we do not receive the answer, then the algorithm does not halt.

Basically, if there is no possible future where the algorithm halts, then we will not be able to send a message back in time. **And the lack of a message means it will not halt.**
gpt
It isn't an area with a lot study. However, it has been argued that a Deutschian closed-time loops allows effectively for the construction of a halt oracle (not by the means you mention but you can read Aaronsen's paper if you want).