Abstract
We will introduce term rewriting by first abstracting from the term structure. In other words, to start, we will concentrate on the so-called abstract reduction systems (ARSs).
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In the computer science literature, a relation without infinite descending chains (i.e., a terminating relation) is often called Noetherian (after the mathematician Emmy Noether, 1882–1935). However, in the mathematical literature, such a relation is usually called Artinian (after the mathematician Emil Artin, 1898–1962) and relations without infinite ascending chains are called Noetherian. In order to avoid confusion, we will not use Noetherian or Artinian notions in this book.
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© 2002 Springer Science+Business Media New York
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Ohlebusch, E. (2002). Abstract Reduction Systems. In: Advanced Topics in Term Rewriting. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-3661-8_2
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DOI: https://doi.org/10.1007/978-1-4757-3661-8_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-2921-1
Online ISBN: 978-1-4757-3661-8
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