We propose a system for monitoring the driving maneuver at road intersections using rule-based reasoning and deep learning-based computer vision techniques. Along with detecting and classifying turning movements online, the system also detects violations such as ignoring STOP signs and failing to yield the right-of-way to other drivers. There is no distinction between temporarily and permanently stopped vehicles in the majority of frameworks proposed in the literature. Therefore, to conduct an accurate right-of-way study, permanently stopped vehicles should be excluded not to confound the results. Moreover, we also propose in this work a low-cost Convolutional Neural Network (CNN)-based object detection framework able to detect moving and temporally stopped vehicles. The detection framework combines the reasoning system with background subtraction and a CNN-based object detector. The obtained results are promising. Compared to the conventional CNN-based methods, the detection framework reduces the execution time of the object detection module by about 30% (i.e., 54.1 instead of 75ms/image) while preserving the same detection reliability. The accuracy of trajectory recognition is 95.32%, that of the zero-speed detection is 96.67%, and the right-of-way detection was perfect.