Advanced Topics in Term Rewriting

the long version

The book is intended for researchers, not only for those working in term rewriting, but it is also of interest for scientists working in areas like functional or logic programming, formal methods, automated reasoning, and symbolic computation, since term rewriting is also a fundamental concept in these areas. For example, Chapter 11 will definitely be of great interest for the logic programming community. In many situations, however, one needs weaker or stronger properties than confluence and termination. In contrast to the current survey articles and textbooks, the so-called confluence and termination hierarchies play a key role in the book. The confluence (termination) hierarchy contains properties related to confluence (termination). In the book, the relationships between the properties in the hierarchies are reviewed, and it is shown that for every implication X => Y in the hierarchies, the property X is undecidable for all term rewriting systems satisfying Y.