Both the Ten Commandments and republicanism influenced "the rule of law" founding belief. This is because the Ten Commandments are based on ten rules that serve to guide the conduct of the Israelites. This is similar to Republicanism which is based on incorporating the rule of law into the system of government that suddenly overruled without legal backings.
the constitution provides that the president "shall have power, by and with the advice and consent of the senate, to make treaties, provided two-thirds of the senators present concur"