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Dynamic specification mining observes program executions to infer models of normal program behavior. What makes us believe that we have seen sufficiently many executions? The TAUTOKO (“Tautoko” is the Mãori word for “enhance, enrich.”) typestate miner generates test cases that cover previously unobserved behavior, systematically extending the execution space, and enriching the specification. To our knowledge, this is the first combination of systematic test case generation and typestate mining-a combination with clear benefits: On a sample of 800 defects seeded into six Java subjects, a static typestate verifier fed with enriched models would report significantly more true positives and significantly fewer false positives than the initial models.