Let R be a binary relation on some domain. Use R∗ for the reflexive transitive closure of R, i.e., the smallest binary relation S with R ⊆ S that is reflexive and transitive. Use R+ for the transitive closure of R, i.e., the smallest binary relation S with R ⊆ S that is transitive. Use I for the identity relation on the domain. Let n range over natural numbers. Define Rn as follows, by induction: R0 := I Rn+1 := R ◦ R...