I don't think the problem is specified precisely enough to have a definite solution. For example, depending on how you specify the stopping condition, the AI might self-modify (or create a new AI) to ignore it. Besides which, I think the most parsimonious solution is to just introduce a resource cost (which would also apply to any agents it makes act on its behalf), which will automatically make it not want to check past a certain point.

I'm also not sure what you intend (rot13) gur qvssrerapr orgjrra "orvat c pregnva" naq "xabjvat lbh'er c pregnva" gb or. Sbe rknzcyr, fnl lbh'er jevgvat n cncre naq lbh ena n grfg naq tbg fgngvfgvpny fvtavsvpnapr (fnl c = 0.01). V gnxr vg va guvf pnfr lbh ner c pregnva, ohg qb lbh xabj lbh'er c pregnva? Frrzf yvxr n jrveq pbaprcg. It's entirely possible that I'm just confused about this aspect, though.