Term rewriting systems are reduction systems in which rewrite rules apply to terms. Terms are built up from variables and constants using function symbols (or operations). Rules of term rewriting systems have the form x->y, where both x and y are terms, x is not a variable, and every variable from y occurs in x as well. A reduction step for term r is defined as follows. If θ is a unifier for r and x, then r is reduced to y θ. If θ is a unifier for r' and x where r' is a subterm of r, then r is reduced to a term obtained from r θ by replacing r' θ with y θ.
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