The phrase "cud-chewing" refers to the process of ruminating or pondering on a particular topic. Some synonyms for this term include contemplation, reflection, musing, and meditation. These words encapsulate the act of deep thought and consideration. Other potential synonyms may include introspection, deliberation, speculation, and rumination. Each term conveys a slightly different nuance of meaning. For instance, introspection implies looking inward and examining one's own thoughts and feelings, while deliberation suggests the act of carefully weighing options and making a decision. Ultimately, the choice of synonym will depend on the context and intended tone of the writing or conversation.