Solving Partial Order Constraints for LPO Termination

TL;DR

This paper presents a novel propositional encoding for reasoning about partial orders, enabling efficient determination of LPO termination in term rewrite systems with significant speed improvements.

Contribution

It introduces a log2 n propositional encoding for partial orders, improving the efficiency of LPO termination analysis in term rewrite systems.

Findings

Orders of magnitude speedups over existing methods

Effective application to LPO termination problems

Generalizable encoding for propositional reasoning about partial orders

Abstract

This paper introduces a new kind of propositional encoding for reasoning about partial orders. The symbols in an unspecified partial order are viewed as variables which take integer values and are interpreted as indices in the order. For a partial order statement on n symbols each index is represented in log2 n propositional variables and partial order constraints between symbols are modeled on the bit representations. We illustrate the application of our approach to determine LPO termination for term rewrite systems. Experimental results are unequivocal, indicating orders of magnitude speedups in comparison with current implementations for LPO termination. The proposed encoding is general and relevant to other applications which involve propositional reasoning about partial orders.