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  "body": "\n## Summary\n\nTerm rewriting replaces the symmetric equations of an equational theory by one-way rules $l \\to r$ that rewrite terms.\nTwo terms are equal in the theory exactly when they are connected by a chain of rule applications in either direction.\nWhen the rules are terminating and confluent, every term has a unique normal form.\nThen two terms are equal in the theory exactly when their normal forms coincide.\nThis turns many word problems for free algebras into a mechanical computation, and the Knuth–Bendix procedure tries to find such rules.\n\n## Explanations\n\n### L1 human\n\nAn equation like $0 + x = x$ can be read as an instruction: wherever $0 + t$ appears, replace it by $t$.\nApplying such instructions until none applies simplifies a term to a normal form.\nIf the instructions always stop and the final answer never depends on the order of the steps, then comparing normal forms decides equality.\nFor example, with the rules $0 + x \\to x$ and $s(x) + y \\to s(x + y)$, the term $s(0) + s(0)$ rewrites to $s(0 + s(0))$ and then to $s(s(0))$.\n",
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