Motivating Example
Consider the rules of regular arithmetic. We can think of these rules as forming a rewriting system. Suppose we are given the expression
We can rewrite this expression in two ways—either simplifying the first bracket, or the second. Simplifying the first bracket, we have
Simplifying the second, gives
We get the same result from rewriting the term in two different ways. This suggests that the rewriting system formed from regular arithmetic is a confluent rewriting system.
Read more about this topic: Confluence (abstract Rewriting)
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