Exercise-based cardiac rehabilitation requires patients to perform a set of certain prescribed exercises a specific number of times. Local muscular endurance exercises are an important part of the rehabilitation program. Automatic exercise recognition and repetition counting, from wearable sensor data, is an important technology to enable patients to perform exercises independently in remote settings, e.g., their own home. In this paper, we first report on a comparison of traditional approaches to exercise recognition and repetition counting (supervised ML and peak detection) with Convolutional Neural Networks (CNNs). We investigated CNN models based on the AlexNet architecture and found that the performance was better than the traditional approaches, for exercise recognition (overall F1-score of 97.18%) and repetition counting (±1 error among 90% observed sets). To the best of our knowledge, our approach of using a single CNN method for both recognition and repetition counting is novel. Also, we make the INSIGHT-LME dataset publicly available to encourage further research.