Many classical normalization procedures in computer algebra—Gaussian elimination, canonicalforms for term algebras, Gröbner bases—can be viewed as instances of a unified process of structuralcollapse E↓, and structural entropy Hstruct in which a potentially vast rewrite space is compressed byeliminating those rewrite rules that do not alter any normal form. This is motivated by utilizing howunique something is relative to adjacent systems to understand its relative complexity. By countingthe number of distinct terms reachable for a given set of rules and an encoded system of terms, wecan quantify its inherent redundancy and compare it to other configurations. Iteratively modifyingrules within the available structure allows us to track the differential effects and follow a path to thesmallest possible count of terms.