Relaxed Weighted Path Order in Theorem Proving

Abstract

We propose an extension of the automated theorem prover E by the weighted path ordering (WPO). WPO is theoretically stronger than all the orderings used in E Prover, however its parametrization is more involved than those normally used in automated reasoning. In particular, it depends on a term algebra. We integrate the ordering in E Prover and perform an evaluation on the standard theorem proving benchmarks. The ordering is complementary to the ones used in E prover so far. Furthermore, first-time presented here, we propose a relaxed variant of the weighted path order as an approximation of the standard WPO definition. A theorem prover strategy with a relaxed order can be incomplete, which is, however, not an issue as completeness can be easily regained by switching to a complete strategy. We show that the relaxed weighted path order can have a huge impact on an improvement of a theorem prover strategy.