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I don't think so. That's assuming the program will always be in a frame of reference which is temporally unbounded. If, for example, it fell into a black hole it would, IIUC, never progress (even locally) beyond the moment of intercepting the event horizon.

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Hmmm, couldn't you, as long as there's a fixed period of time that supports time travel, keep execution working by travelling to the start of the period again and again (/with/ the current program state) to avoid the program from going beyond the working time period?

Ooh, clever. Vaguely envision entropy problems, that some mash-up of Godel's Incompleteness theorem, Maxwell's Demon, and Bell's Inequality, and Newton's laws conspires against it. Maybe sending changes back add entropy, or moves it around? Would make a good old-school SF story, with backwater multi-verse dumps for waste entropy, a free-lance troubleshooter uncovering a secret corporate scandal regarding deleterious effects, etc.

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