Decision Procedures for Loop Detection

The dependency pair technique is a powerful modular method for automated termination proofs of term rewrite systems. We first show that dependency pairs are also suitable for disproving termination: loops can be detected more easily. In a second step we analyze how to disprove innermost termination. Here, we present a novel procedure to decide whether a given loop is an innermost loop. All results have been implemented in the termination prover AProVE.