We show how the paradigm of learning-based testing (LBT) can be applied to automate specification-based black-box testing of reactive systems using term rewriting technology. A general model for a reactive system can be given by an extended Mealy automata (EMA) over an abstract data type (ADT). A finite state EMA over an ADT can be efficiently learned in polynomial time using the CGE regular inference algorithm, which builds a compact representation as a complete term rewriting system. We show how this rewriting system can be used to model check the learned automaton against a temporal logic specification by means of narrowing. Combining CGE learning with a narrowing model checker we obtain a new and general architecture for learning-based testing of reactive systems. We compare the performance of this LBT architecture against random testing using a case study.