Semi-automatic schema matching systems have been developed to compute mapping suggestions that can be corrected by a user. However, constructing and tuning match strategies still requires a high manual effort. We therefore propose a self-configuring schema matching system that is able to automatically adapt to the given mapping problem at hand. Our approach is based on analyzing the input schemas as well as intermediate match results. A variety of matching rules use the analysis results to automatically construct and adapt an underlying matching process for a given match task. The evaluation shows that our system is able to robustly return good quality mappings across different mapping problems and domains.