Automating the Knuth Bendix ordering

Dick, Jeremy; Kalmus, John; Martin, Ursula

doi:10.1007/bf01237233

Cited by 37 publications

(30 citation statements)

References 12 publications

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“…We have yet to carry out a practical investigation of the technique: it would have many similarities with the technique for using the simplex method to identify weights for the Knuth-Bendix ordering (Dick et al, 1990).…”

Section: The General Frameworkmentioning

confidence: 99%

Invariants, Patterns and Weights for Ordering Terms

Martin

Shand

2000

Journal of Symbolic Computation

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We prove that any simplification order over arbitrary terms is an extension of an order by weight, by considering a related monadic term algebra called the spine. We show that any total ground-stable simplification order on the spine lifts to an order on the full term algebra. Conversely, under certain restrictions, a simplification ordering on the term algebra defines a weight function on the spine, which in turn can be lifted to a weight order on the original ground terms which contains the original order. We investigate the Knuth-Bendix and polynomial orders in this light. We provide a general framework for ordering terms by counting embedded patterns, which gives rise to many new orderings. We examine the recursive path order in this context.

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Section: The General Frameworkmentioning

confidence: 99%

Invariants, Patterns and Weights for Ordering Terms

Martin

Shand

2000

Journal of Symbolic Computation

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“…AProVE also offers Knuth-Bendix orders (KBO, [20]) using the polynomial-time algorithm of [21] and the technique of [9] to compute the degenerate subsystem of homogeneous linear inequalities.…”

Section: Direct Termination Proofsmentioning

confidence: 99%

Automated Termination Proofs with AProVE

Giesl

Thiemann

Schneider–Kamp

et al. 2004

Rewriting Techniques and Applications

110

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Abstract. We describe the system AProVE, an automated prover to verify (innermost) termination of term rewrite systems (TRSs). For this system, we have developed and implemented efficient algorithms based on classical simplification orders, dependency pairs, and the size-change principle. In particular, it contains many new improvements of the dependency pair approach that make automated termination proving more powerful and efficient. In AProVE, termination proofs can be performed with a user-friendly graphical interface and the system is currently among the most powerful termination provers available.

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“…In this paper we presented two logic-based encodings of KBO-pure SAT and PBC-which can be implemented more efficiently and with considerably less effort than the methods described in [5,15]. Especially the PBC encoding gives rise to a very fast implementation even without caring about possible optimizations in the encoding.…”

Section: Discussionmentioning

confidence: 99%

“…T T T admits only strict precedences, AProVE also quasi-precedences. Both implement the polynomial time algorithm of Korovin and Voronkov [15] together with techniques of Dick et al [5]. We used the 865 TRSs which do not specify any strategy or theory and the 322 string rewrite systems (SRSs) in version 3.2 of the Termination Problem Data Base [18].…”

Section: Resultsmentioning

confidence: 99%

“…1 We know of only two termination tools that contain an implementation of KBO, AProVE [11] and T T T [12], but neither of these tools incorporate KBO in their fully automatic mode for the TRS category. This is perhaps due to the fact that the algorithms known for deciding KBO orientability ( [5,15]) are not easy to implement efficiently, despite the fact that the problem is known to be decidable in polynomial time [15]. The aim of this paper is to make KBO a more attractive choice for termination tools by presenting two simple encodings of KBO orientability into (pseudo-)propositional logic such that checking satisfiability of the resulting formula amounts to proving KBO termination.…”

Section: Introductionmentioning

confidence: 99%

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Satisfying KBO Constraints

Zankl

Middeldorp

Lecture Notes in Computer Science

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Abstract. This paper presents two new approaches to prove termination of rewrite systems with the Knuth-Bendix order efficiently. The constraints for the weight function and for the precedence are encoded in (pseudo-)propositional logic and the resulting formula is tested for satisfiability. Any satisfying assignment represents a weight function and a precedence such that the induced Knuth-Bendix order orients the rules of the encoded rewrite system from left to right.

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Automating the Knuth Bendix ordering

Cited by 37 publications

References 12 publications

Invariants, Patterns and Weights for Ordering Terms

Invariants, Patterns and Weights for Ordering Terms

Automated Termination Proofs with AProVE

Satisfying KBO Constraints

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