Decreasing Diagrams and Relative Termination

Abstract

In this article we use the decreasing diagrams technique to show that a left-linear and locally confluent term rewrite system $\mathcal{R}$ is confluent if the critical pair steps are relatively terminating with respect to $\mathcal{R}$ . We further show how to encode the rule-labeling heuristic for decreasing diagrams as a satisfiability problem. Experimental data for both methods are presented.