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 X n with n elements. Namely, we consider the monoids OR n and POR n of all full, respectively partial, transformations on X n that preserve or reverse the orientation, as well as their respective submonoids OP n and POP n of all orientation-preserving elements. The inverse monoid PORI n of all injective elements of POR n is also considered.