What are international rules that have become binding through consistent and longstanding behavior called?

The correct answer is Customary International Law. This term refers to a form of international law that emerges from the consistent practices and behaviors of states that are recognized as obligatory and legally binding. Over time, certain practices become accepted as law when they are repeated consistently by a significant number of states, and these practices must also be acknowledged as a legal obligation, which is often expressed in the concept of opinio juris.

Statutory Law, while important, relates to laws enacted by legislative bodies within a specific jurisdiction and does not encompass the broader, unwritten practices that arise from customary behavior among countries. Treaties are formal agreements between states that are legally binding but are distinct from customary practices. Conventions can refer to treaties or agreements, often with specific themes, but they do not specifically denote the binding nature derived solely from consistent state behavior. Customary International Law embodies the principles that arise from states' actions and is acknowledged and accepted as a norm, making it the correct answer in this context.