## Term Rewriting and All ThatThis textbook offers a unified, self-contained introduction to the field of term rewriting. Baader and Nipkow cover 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. They present the main algorithms both informally and as programs in the functional language Standard ML (An appendix contains a quick and easy introduction to ML). Key chapters cover crucial algorithms such as unification and congruence closure in more depth and develop efficient Pascal programs. The book contains many examples and over 170 exercises. This is also an ideal reference book for professional researchers: results spread over many conference and journal articles are collected here in a unified notation, detailed proofs of almost all theorems are provided, and each chapter closes with a guide to the literature. |

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### Contents

II | 1 |

III | 7 |

IV | 13 |

V | 16 |

VI | 18 |

VII | 21 |

VIII | 26 |

IX | 28 |

XXXVI | 160 |

XXXVII | 164 |

XXXVIII | 172 |

XXXIX | 178 |

XL | 182 |

XLI | 184 |

XLII | 187 |

XLIII | 189 |

X | 33 |

XI | 34 |

XII | 47 |

XIII | 49 |

XV | 58 |

XVI | 59 |

XVII | 61 |

XVIII | 62 |

XIX | 65 |

XX | 71 |

XXI | 73 |

XXII | 79 |

XXIII | 82 |

XXIV | 91 |

XXV | 93 |

XXVI | 101 |

XXVII | 104 |

XXVIII | 111 |

XXIX | 131 |

XXX | 134 |

XXXI | 135 |

XXXII | 145 |

XXXIII | 151 |

XXXIV | 157 |

XXXV | 158 |

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### Common terms and phrases

AC-unifier algebra algorithm alien subterms applied arbitrary assume binary Boolean Boolean rings Buchberger's algorithm C-unification coefficient collapsing computation confluent congruence closure contains critical pairs decidable decision procedure defined definition denote E-algebra elements equational theory equivalent example Exercise exists finite set free algebra function symbols functional programming ground terms halting problem hence holds homomorphism idempotent implementation implies induction infinite joinable Knuth-Bendix order left-linear Lemma lexicographic path order linear minimal complete set modulo monomial multiset nodes nontrivial normal form obtained occurs check orthogonal partial order proof prove recursive reduction order relation rewrite rule satisfies set of identities set of variables signature simplification order Sj-i solution step strict order substitution term rewriting system termination Theorem trivial Turing machine unary function unary function symbol undecidable unification problem unifier Var(t well-founded word problem yields