term rewriting system


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term rewriting system

(TRS) A collection of rewrite rules used to transform terms (expressions, strings in some formal language) into equivalent terms. See reduction.
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Consider the following term rewriting system for subtraction:
X - 0 [right arrow] X [R.sub.1] s(X) - s(Y) [right arrow] X - Y [R.sub.2] This term rewriting system is inductively sequential and a definitional tree, T, of the operation "-" has an exempt node for the pattern 0 - s(X), i.e., the system is incomplete and ([Lambda], ?, { }) [element of] [Lambda](0 - s(X), T).
Let R be a term rewriting system without rules for [approximately equals] and [conjunction].