A Transformation System for Developing Recursive Programs
Journal of the ACM (JACM)
Journal of Automated Reasoning
Rules and Strategies for Program Transformation
Proceedings of the IFIP TC2/WG 2.1 State-of-the-Art Report on Formal Program Development
On the Evaluation of Indexing Techniques for Theorem Proving
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
Combining superposition, sorts and splitting
Handbook of automated reasoning
The design and implementation of VAMPIRE
AI Communications - CASC
AI Communications - CASC
AI Communications - CASC
An extension of the Knuth-Bendix ordering with LPO-like properties
LPAR'07 Proceedings of the 14th international conference on Logic for programming, artificial intelligence and reasoning
On transfinite Knuth-Bendix orders
CADE'11 Proceedings of the 23rd international conference on Automated deduction
The CADE-23 Automated Theorem Proving System Competition - CASC-23
AI Communications
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The Knuth---Bendix ordering (KBO) is one of the term orderings in widespread use. We present a new algorithm to compute KBO, which is (to our knowledge) the first asymptotically optimal one. Starting with an `obviously correct' version, we use program transformation to stepwise develop an efficient version, making clear the essential ideas, while retaining correctness. By theoretical analysis we show that the worst-case behavior is thereby changed from quadratic to linear. Measurements show the practical improvements of the different variants.