Analyzing Innermost Runtime Complexity Through Tuple Interpretations

Time complexity in rewriting is naturally understood as the number of steps needed to reduce terms normal forms. Establishing bounds this measure a well-known problem community. A vast majority techniques find such consist modifying termination proofs order recover information. This has been done for instance with semantic interpretations, recursive path orders, and dependency pairs. In paper, we follow same program by tailoring tuple interpretations deal innermost analysis. interpretation interprets tuples holding upper cost reduction size contrast full setting, strongly monotonic requirement components dropped when reductions are innermost. weakened on allows us prove version compatibility result: if all rules term system can be strictly oriented, then rewrite relation well-founded. We establish necessary conditions which guarantee polynomial runtime compatible systems describe search procedure interpretations.