Solving partial order constraints for LPO termination

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 ⌈log2n⌉ 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.