LASTS is a framework that can explain the decisions of black box models for time series classification. The explanation consists of factual and counterfactual rules revealing the reasons for the classification through conditions expressed as subsequences that must or must not be contained in the time series. In addition, a set of exemplar and counterexemplar time series highlight similarities and differences with the time series under analysis. A wide experimentation shows that the proposed method provides faithful, meaningful, stable, and interpretable explanations. Besides, we show that the proposed explainer can be employed on multivariate time series.