We develop a quantitative framework in order to understand how OR parallelism can be used to reduce execution times in parallel computer algebra programs.  In order to best understand the issues that pertain to OR parallelism, we restrict the investigation to its use on a single processor: How does running the tasks in parallel on a uniprocessor affect the execution time? Once this question has been addressed, then using a multiprocessor to exploit OR parallelism is not substantially different than using it to exploit AND parallelism.