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CMP.13:2 - Problem

How can a calculation discard detail yet retain a justified answer to the property being asked, and recover the distinctions that an inconclusive answer exposes?

A summary can combine possibilities that never occur together. A sequence of individually possible transitions can then appear to be an executable path. Conversely, retaining every distinction may make the supposedly cheaper calculation as difficult as the original. Loops add another difficulty: successive summaries can keep changing even when each update is easy.