A system in which words (expressions) of a formal language can be transformed according to a finite set of rewrite rules is called a reduction system. While reduction systems are also known as string rewriting systems or term rewriting systems, the term "reduction system" is more general. Lambda calculus is an example of a reduction system with lambda conversion rules constituting its rewrite rules. If none of the rewrite rules of a reduction system apply to expression E, then E is said to be in normal form for a reduction system. A pair of expressions (x, y) is called joinable if both x and y can be reduced to the same expression in zero or more reduction steps (i.e., applications of rewrite rules).
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