Example 1. 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". Observe that these rules can be applied to both "a" and "b" in any fashion to get the term "c". Such a property is clearly an important one. In a sense, "c" is a "simplest" term in the system, since nothing can be applied to "c" to transform it any further. This example leads us to define some important notions in the general setting of an ARS. First we need some basic notions and notations.