Graph rewriting rules may be used as a graphical equivalent of term rewriting rules. Given a term, it is clear how to express it as a labeled, ordered tree. Moreover, if there are common subterms, one wishes to exploit this fact by combining subtrees, thereby obtaining an equivalent directed, acyclic graph which is a more compact representation of the term. This compaction saves spaces and also simplifies the problem of repeated variable occurrences which must be substituted consistently.

The compressed representation of terms introduces certain difficulties into the category-theoretical machinery that have been used to formalize graph rewriting systems. The paper discusses how a previously developed formalism cannot cope with this difficulty, as well as the alternative proposed.