## 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 |

XXXV | 160 |

XXXVI | 164 |

XXXVII | 172 |

XXXVIII | 178 |

XXXIX | 182 |

XL | 184 |

XLI | 187 |

XLII | 189 |

X | 33 |

XI | 34 |

XII | 47 |

XIII | 49 |

XIV | 58 |

XV | 59 |

XVI | 61 |

XVII | 62 |

XVIII | 65 |

XIX | 71 |

XX | 73 |

XXI | 79 |

XXII | 82 |

XXIII | 91 |

XXIV | 93 |

XXV | 101 |

XXVI | 104 |

XXVII | 111 |

XXVIII | 131 |

XXIX | 134 |

XXX | 135 |

XXXI | 145 |

XXXII | 151 |

XXXIII | 157 |

XXXIV | 158 |

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### Common terms and phrases

addition algebra algorithm applied arbitrary assume basic C-unification called closed closure collapsing completion completion procedure computation confluent congruence consequence consider constants contains corresponding critical pairs decidable decision defined definition denote direction easy elements equational equivalent example Exercise exists extended fact finite function symbols given ground hence holds homomorphism identities implementation implies induction infinite instance integer interpretation Lemma lexicographic linear mapping means minimal monomial multiset normal form Note obtained Obviously occurs orthogonal polynomial position problem programming proof prove reduction reduction order relation replaced requires result rules satisfies sequence set of identities shown signature solution solved step strict substitution subterm term rewriting system termination Theorem theory trivial true turn unification unifier variables write yields

### References to this book

Software Engineering with OBJ: Algebraic Specification in Action Joseph A. Goguen,Grant Malcolm No preview available - 2000 |

Isabelle/HOL: A Proof Assistant for Higher-Order Logic Tobias Nipkow,Lawrence C. Paulson,Markus Wenzel No preview available - 2002 |