In mathematics, computer science and logic, overlap, as a property of the reduction rules in term rewriting system, describes a situation where a number of different reduction rules specify potentially contradictory ways of reducing a reducible expression, also known as a redex, within a term.
[1] More precisely, if a number of different reduction rules share function symbols on the left-hand side, overlap can occur.
Often we do not consider trivial overlap with a redex and itself.
The result of reducing different redexes is described in a what is known as a critical pair; the critical pair arising out of this term rewriting system is
Overlap may occur with fewer than two reduction rules.
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