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Methods of proving that a term-rewriting system terminates are presented. They are based on the notion of "simplification orderings", orderings in which any term that is homeomorphically embeddable in another is smaller than the other. A particularly useful class of simplification orderings, the "recursive path orderings", is defined. Several examples of… (More)

A common tool for proving the termination of programs is the <italic>well-founded set</italic>, a set ordered in such a way as to admit no infinite descending sequences. The basic approach is to find a <italic>termination function</italic> that maps the values of the program variables into some well-founded set, such that the value of the termination… (More)

Church's Thesis asserts that the only numeric functions that can be calculated by effective means are the recursive ones, which are the same, extensionally, as the Turing-computable numeric functions. The Abstract State Machine Theorem states that every classical algorithm is behaviorally equivalent to an abstract state machine. This theorem presupposes… (More)

1 I n t r o d u c t i o n Interest in the theory and applications of rewriting has been growing rapidly, as evidenced in part by four conference proceedings (including this one) To encourage and stimulate continued progress in this area, we have collected (with the help of colleagues) a number of problems that appear to us to be of interest and regarding… (More)

We propose a novel unsupervised method for separating out distinct authorial components of a document. In particular, we show that, given a book artificially " munged " from two thematically similar biblical books, we can separate out the two constituent books almost perfectly. This allows us to automatically recapitulate many conclusions reached by Bible… (More)

We p r e s e n t an unfailing" extension of the standard Knuth-Bendix completion procedure that is guaranteed to produce a desired canon-ical system, provided certain conditions are met. We p r o ve that this unfailing completion method is refutationally complete for theorem proving in equational theories. The method can also be applied to Horn clauses with… (More)

We describe the application of proof orderings—a technique for reasoning about inference systems-to various rewrite-based theorem-proving methods, including refinements of the standard Knuth-Bendix completion procedure based on critical pair criteria; Huet's procedure for rewriting modulo a congruence; ordered completion (a refutationally complete… (More)