 In this case, the elements of the set are usually referred to as "executions" of the system.The name "prefix order" stems from the prefix order on words, which is a special kind of substring relation and, because of its discrete character, a tree.A prefix order is a binary relation "≤" over a set "P" which is antisymmetric, transitive, reflexive, and downward total, i.e., for all "a", "b", and "c" in "P", we have that