The word "ex-postulating" is quite uncommon and specific in nature, meaning the act of making a detailed analysis after the fact. However, there are several other terms that could be used as synonyms. For instance, "retrospect", "review", and "reappraisal" all convey a similar meaning of looking back on something and analyzing it in detail. "Post-mortem", "autopsy" and "investigation" could also be considered synonyms in certain contexts. Other options include terms like "aftermath", "examination", and "evaluation", depending on the specific context of use. Ultimately, it's important to choose the appropriate synonym to accurately convey the intended meaning.