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The first requirement says that any variable substitution scheme we apply should result in a simple top-level expression. The second requirement ensures that the top-level expression conveys as much information as possible. In addition, it ensures that the renderings resulting from variable substitution do not end up being more complicated than plain renderings. Thus, in eq:integral, substituting identifier [tex2html_wrap5810] for the entire right-hand side to produce

i equals x where x equals [tex2html_wrap5812]does not simplify the rendering. This is because the top-level expression is a relation, and substituting for one of the sides of a relation only produces a new relation which is as complex as the original. The third requirement ensures that all expressions are compared using the same weighting scheme. Measure

We introduce the notion of *relative complexity* below:

Thu Mar 9 20:10:41 EST 1995