## Term Rewriting and All ThatThis textbook offers a unified and self-contained introduction to the field of term rewriting. It covers all the basic material (abstract reduction systems, termination, confluence, completion, and combination problems), but also some important and closely connected subjects: universal algebra, unification theory, Gröbner bases and Buchberger's algorithm. The main algorithms are presented both informally and as programs in the functional language Standard ML (an appendix contains a quick and easy introduction to ML). Certain crucial algorithms like unification and congruence closure are covered in more depth and Pascal programs are developed. The book contains many examples and over 170 exercises. This text is also an ideal reference book for professional researchers: results that have been spread over many conference and journal articles are collected together in a unified notation, proofs of almost all theorems are provided, and each chapter closes with a guide to the literature. |

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AC1unifier algorithm applied arbitrary assume basic completion procedure binary called coefficient computation confluent congruence closure contains convergent critical pairs Cunification decidable decision procedure defined definition denotes diamond property elements equational theory equivalent Eunifiers example Exercise exists finite set free algebra functional programming graph Gröbner Gröbner bases ground terms halting problem Hence holds homomorphism Huet’s idempotent implementation implies induction input joinable KnuthBendix order lefthand side leftlinear Lemma lexicographic path order lexicographic product linear monomial multiset nodes normal form obtain Obviously occurs check orthogonal partial order polynomial interpretation polynomial order position quotient algebra redex reduction order relation rewrite rules root symbol satisfies set of identities set of variables signature simplification order solution Spolynomials SpringerVerlag strict order subterm property syntactic term rewriting systems Theorem trivial Turing machine unary function unary function symbols undecidable unification problem unifier wellfounded word problem yields