Congruences on monoids of transformations preserving the orientation on a finite chain

The main subject of this paper is the description of the congruences on certain monoids of transformations on a finite chain Xn with n elements. Namely, we consider the monoids ORn and PORn of all full, respectively partial, transformations on Xn that preserve or reverse the orientation, as well as their respective submonoids OPn and POPn of all orientation-preserving elements. The inverse monoid PORIn of all injective elements of PORn is also considered.