Stemming and thesaurus equivalences generally introduce little memory overhead (beyond the amount of memory required to store the raw string forms of the equivalences).
In terms of online processing, both features expand the set of results for typical user queries.
While this generally slows search performance (search operations require an amount of time that grows linearly with the number of results), typically these additional results are a required part of the application behavior and cannot be avoided.
The overhead involved in matching the user query to thesaurus and stemming forms is generally low, but could slow performance in cases where a large thesaurus (tens of thousands of entries) is asked to process long search queries (dozens of terms).
Because matching for stemming entries is performed on a single-word basis, the cost for stemming-oriented query expansion does not grow with the size of the stemming database or with the length of the query. However, the stemming performance of a specific language is affected by the degree to which the language is inflected. For example, German nouns are much more inflected than English nouns.