 The focus of the study, and the terminology are different however.In a state transition system one is interested in interpreting the labels as actions, whereas in an ARS the focus is on how objects may be transformed (rewritten) into others.Suppose the set of objects is "T" = {"a", "b", "c"} and the binary relation is given by the rules "a" → "b", "b" → "a", "a" → "c", and "b" → "c".