diff --git a/Boolean_set_operations_2/doc/Boolean_set_operations_2/Boolean_set_operations_2.txt b/Boolean_set_operations_2/doc/Boolean_set_operations_2/Boolean_set_operations_2.txt
index d03add5708a..cb0527fe30f 100644
--- a/Boolean_set_operations_2/doc/Boolean_set_operations_2/Boolean_set_operations_2.txt
+++ b/Boolean_set_operations_2/doc/Boolean_set_operations_2/Boolean_set_operations_2.txt
@@ -669,10 +669,10 @@ The traits class used to instantiate the `General_polygon_set_2`
 class template must model the concept `GeneralPolygonSetTraits_2`,
 and is tailored to handle a specific family of curves. The concept
 `GeneralPolygonSetTraits_2` refines the concept
-`ArrangementDirectionalXMonotoneTraits_2` specified next.
+`AosDirectionalXMonotoneTraits_2` specified next.
 
-The concept `ArrangementDirectionalXMonotoneTraits_2` refines the
-concept `ArrangementXMonotoneTraits_2` (see
+The concept `AosDirectionalXMonotoneTraits_2` refines the
+concept `AosXMonotoneTraits_2` (see
 Section \ref arr_sssecinsert_x_mon in the 2D Arrangements package).
 Thus, a model of this concept must define the type `X_monotone_curve_2`,
 which represents an \f$ x\f$-monotone curve, and the type `Point_2`,
@@ -687,7 +687,7 @@ curve is not required to have a designated <I>source</I> and <I>target</I>, it i
 smaller) and the right (lexicographically larger) endpoints of a given
 curve.
 
-The `ArrangementDirectionalXMonotoneTraits_2` concept treats its
+The `AosDirectionalXMonotoneTraits_2` concept treats its
 \f$ x\f$-monotone curves as directed objects. It thus requires two additional
 operations on \f$ x\f$-monotone curves:
 <UL>
@@ -702,10 +702,10 @@ The traits classes `Arr_segment_traits_2`,
 `Arr_conic_traits_2` and `Arr_rational_function_traits_2`, which are
 bundled in the `Arrangement_2` package and distributed with \cgal,
 are all models of the refined concept
-`ArrangementDirectionalXMonotoneTraits_2`.\cgalFootnote{The \cgalFootnoteCode{Arr_polyline_traits_2} class is <I>not</I> a model of the, \cgalFootnoteCode{ArrangementDirectionalXMonotoneTraits_2} concept, as the \f$ x\f$-monotone curve it defines is always directed from left to right. Thus, an opposite curve cannot be constructed. However, it is not very useful to construct a polygon whose edges are polylines, as an ordinary polygon with linear edges can represent the same entity.}
+`AosDirectionalXMonotoneTraits_2`.\cgalFootnote{The \cgalFootnoteCode{Arr_polyline_traits_2} class is <I>not</I> a model of the, \cgalFootnoteCode{AosDirectionalXMonotoneTraits_2} concept, as the \f$ x\f$-monotone curve it defines is always directed from left to right. Thus, an opposite curve cannot be constructed. However, it is not very useful to construct a polygon whose edges are polylines, as an ordinary polygon with linear edges can represent the same entity.}
 
 Just as with the case of computations using models of the
-`ArrangementXMonotoneTraits_2` concept, operations are robust only
+`AosXMonotoneTraits_2` concept, operations are robust only
 when exact arithmetic is used. When inexact arithmetic is used,
 (nearly) degenerate configurations may result in abnormal termination
 of the program or even incorrect results.
@@ -761,7 +761,7 @@ curves.
 The class-template `General_polygon_2<ArrDirectionalXMonotoneTraits>`
 models the concept `GeneralPolygon_2`. Its sole template parameter
 must be instantiated with a model of the concept
-`ArrangementDirectionalXMonotoneTraits_2` from which it obtains the
+`AosDirectionalXMonotoneTraits_2` from which it obtains the
 `X_monotone_curve_2` type. It uses the geometric operations
 on this type provided by such a model to maintain a container of
 directed curves of type `X_monotone_curve_2`, which represents a
@@ -772,7 +772,7 @@ The class-template
 models the concept `GeneralPolygonSetTraits_2`, and can be used to
 instantiate the class template `General_polygon_set_2`.
 It serves as an adapter for a geometric traits class, which models the
-concept `ArrangementDirectionalXMonotoneTraits_2`.
+concept `AosDirectionalXMonotoneTraits_2`.
 It can be used for performing set-operations on general polygons.
 The implementation of the adapter is rather simple, as it is derived
 from the instantiated template-parameter `ArrXMonotoneTraits_2`
@@ -781,13 +781,13 @@ the methods provided by the instantiated parameter
 `GeneralPolygon`, which is a model of the concept
 `GeneralPolygon_2`. By default, the `GeneralPolygon` parameter
 is defined as
-`General_polygon_2<ArrangementDirectionalXMonotoneTraits_2>`.
+`General_polygon_2<AosDirectionalXMonotoneTraits_2>`.
 
 The code excerpt listed below defines a general-polygon set type that
 can be used to perform Boolean set-operations on point sets bounded by
 the \f$ x\f$-monotone curve type defined by the arrangement-traits class
 `Arr_traits_2`, which is some representative model of the concept
-`ArrangementDirectionalXMonotoneTraits_2`.
+`AosDirectionalXMonotoneTraits_2`.
 
 \code{.cpp}
 #include <CGAL/General_polygon_2.h>
diff --git a/Boolean_set_operations_2/doc/Boolean_set_operations_2/CGAL/Boolean_set_operations_2.h b/Boolean_set_operations_2/doc/Boolean_set_operations_2/CGAL/Boolean_set_operations_2.h
index 39faf23e21a..4fd5c2c9e38 100644
--- a/Boolean_set_operations_2/doc/Boolean_set_operations_2/CGAL/Boolean_set_operations_2.h
+++ b/Boolean_set_operations_2/doc/Boolean_set_operations_2/CGAL/Boolean_set_operations_2.h
@@ -90,7 +90,7 @@ void complement(const Polygon_2<Kernel, Container>& pgn,
  * \param pgn the input polygon.
  * \param res the complement of \p pgn.
  * \pre `%ArrTraits` must be a model of the concept
- *      `ArrangementDirectionalXMonotoneTraits_2`.
+ *      `AosDirectionalXMonotoneTraits_2`.
  */
 template <typename ArrTraits>
 void
@@ -136,7 +136,7 @@ OutputIterator complement(const Polygon_with_holes_2<Kernel, Container>& pgn,
  *             `General_polygon_with_holes_2<<General_polygon_2<ArrTraits>>`.
  * \return the past-the-end iterator of the output container.
  * \pre `%ArrTraits` must be a model of the concept
- *      `ArrangementDirectionalXMonotoneTraits_2`.
+ *      `AosDirectionalXMonotoneTraits_2`.
  */
 template <typename ArrTraits, typename OutputIterator>
 OutputIterator
@@ -161,7 +161,7 @@ void complement(const Polygon_2<Kernel, Container>& pgn,
  * \param res the resulting complement of \p pgn
  * \param traits a traits object.
  * \pre `%ArrTraits` must be a model of the concept
- *      `ArrangementDirectionalXMonotoneTraits_2`.
+ *      `AosDirectionalXMonotoneTraits_2`.
  * \pre `GpsTraits` must be a model of the concept `GeneralPolygonSetTraits_2`.
  */
 template <typename ArrTraits, typename GpsTraits>
@@ -193,7 +193,7 @@ OutputIterator complement(const Polygon_with_holes_2<Kernel, Container>& pgn,
  * \param traits a traits object.
  * \return the past-the-end iterator of the output container.
  * \pre `%ArrTraits` must be a model of the concept
- *      `ArrangementDirectionalXMonotoneTraits_2`.
+ *      `AosDirectionalXMonotoneTraits_2`.
  * \pre `GpsTraits` must be a model of the concept `GeneralPolygonSetTraits_2`.
  */
 template <typename Polygon, typename OutputIterato, typename GpsTraitsr>
@@ -438,7 +438,7 @@ OutputIterator difference(const Polygon_with_holes_2<Kernel, Container>& pgn1,
  *           Its dereference type must be convertibe to
  *             `General_polygon_with_holes_2<General_polygon_2<ArrTraits>>`.
  * \return the past-the-end iterator of the output container.
- * \pre `%ArrTraits` must be a model of the concept `ArrangementDirectionalXMonotoneTraits_2`.
+ * \pre `%ArrTraits` must be a model of the concept `AosDirectionalXMonotoneTraits_2`.
  */
 template <typename ArrTraits, typename OutputIterator>
 OutputIterator difference(const General_polygon_2<ArrTraits>& pgn1,
@@ -454,7 +454,7 @@ OutputIterator difference(const General_polygon_2<ArrTraits>& pgn1,
  *             `General_polygon_with_holes_2<General_polygon_2<ArrTraits>>`.
  * \return the past-the-end iterator of the output container.
  * \pre `%ArrTraits` must be a model of the concept
- *      `ArrangementDirectionalXMonotoneTraits_2`.
+ *      `AosDirectionalXMonotoneTraits_2`.
  */
 template <typename ArrTraits, typename OutputIterator>
 OutputIterator
@@ -471,7 +471,7 @@ difference(const General_polygon_with_holes_2<General_polygon_2<ArrTraits>>& pgn
  *             `General_polygon_with_holes_2<General_polygon_2<ArrTraits>>`.
  * \return the past-the-end iterator of the output container.
  * \pre `%ArrTraits` must be a model of the concept
- *      `ArrangementDirectionalXMonotoneTraits_2`.
+ *      `AosDirectionalXMonotoneTraits_2`.
  */
 template <typename ArrTraits, typename OutputIterator>
 OutputIterator
@@ -578,7 +578,7 @@ OutputIterator difference(const Polygon_with_holes_2<Kernel, Container>& pgn1,
  * \param traits a traits object.
  * \return the past-the-end iterator of the output container.
  * \pre `%ArrTraits` must be a model of the concept
- *      `ArrangementDirectionalXMonotoneTraits_2`.
+ *      `AosDirectionalXMonotoneTraits_2`.
  * \pre GpsTraits must be a model of `GeneralPolygonSetTraits_2`.
  */
 template <typename ArrTraits, typename OutputIterator, typename GpsTraits>
@@ -597,7 +597,7 @@ OutputIterator difference(const General_polygon_2<ArrTraits>& pgn1,
  * \param traits a traits object.
  * \return the past-the-end iterator of the output container.
  * \pre `%ArrTraits` must be a model of the concept
- *      `ArrangementDirectionalXMonotoneTraits_2`.
+ *      `AosDirectionalXMonotoneTraits_2`.
  * \pre GpsTraits must be a model of `GeneralPolygonSetTraits_2`.
  */
 template <typename ArrTraits, typename OutputIterator, typename GpsTraits>
@@ -617,7 +617,7 @@ difference(const General_polygon_with_holes_2<General_polygon_2<ArrTraits>>& pgn
  * \param traits a traits object.
  * \return the past-the-end iterator of the output container.
  * \pre `%ArrTraits` must be a model of the concept
- *      `ArrangementDirectionalXMonotoneTraits_2`.
+ *      `AosDirectionalXMonotoneTraits_2`.
  * \pre GpsTraits must be a model of `GeneralPolygonSetTraits_2`.
  */
 template <typename ArrTraits, typename OutputIterator, typename GpsTraits>
@@ -858,7 +858,7 @@ bool do_intersect(const Polygon_with_holes_2<Kernel, Container>& pgn1,
  * \return `true` if `pgn1` and `pgn2` intersect in their interior and `false`
  *         otherwise.
  * \pre `%ArrTraits` must be a model of the concept
- *      `ArrangementDirectionalXMonotoneTraits_2`.
+ *      `AosDirectionalXMonotoneTraits_2`.
  */
 template <typename ArrTraits>
 bool do_intersect(const General_polygon_2<ArrTraits>& pgn1,
@@ -870,7 +870,7 @@ bool do_intersect(const General_polygon_2<ArrTraits>& pgn1,
  * \return `true` if `pgn1` and `pgn2` intersect in their interior and `false`
  *         otherwise.
  * \pre `%ArrTraits` must be a model of the concept
- *      `ArrangementDirectionalXMonotoneTraits_2`.
+ *      `AosDirectionalXMonotoneTraits_2`.
  */
 template <typename ArrTraits>
 bool
@@ -883,7 +883,7 @@ do_intersect(const General_polygon_2<ArrTraits>& pgn1,
  * \return `true` if `pgn1` and `pgn2` intersect in their interior and `false`
  *         otherwise.
  * \pre `%ArrTraits` must be a model of the concept
- *      `ArrangementDirectionalXMonotoneTraits_2`.
+ *      `AosDirectionalXMonotoneTraits_2`.
  */
 template <typename ArrTraits>
 bool do_intersect(const General_polygon_with_holes_2<General_polygon_2<ArrTraits>>& pgn1,
@@ -1058,7 +1058,7 @@ bool do_intersect(const Polygon_with_holes_2<Kernel, Container>& pgn1,
  *         otherwise.
  * \pre `GpsTraits` must be a model of the concept `GeneralPolygonSetTraits_2`.
  * \pre `%ArrTraits` must be a model of the concept
- *      `ArrangementDirectionalXMonotoneTraits_2`.
+ *      `AosDirectionalXMonotoneTraits_2`.
  */
 template <typename ArrTraits, typename GpsTraits>
 bool do_intersect(const General_polygon_2<ArrTraits>& pgn1,
@@ -1073,7 +1073,7 @@ bool do_intersect(const General_polygon_2<ArrTraits>& pgn1,
  *         otherwise.
  * \pre `GpsTraits` must be a model of the concept `GeneralPolygonSetTraits_2`.
  * \pre `%ArrTraits` must be a model of the concept
- *      `ArrangementDirectionalXMonotoneTraits_2`.
+ *      `AosDirectionalXMonotoneTraits_2`.
  */
 template <typename ArrTraits, typename GpsTraits>
 bool
@@ -1089,7 +1089,7 @@ do_intersect(const General_polygon_2<ArrTraits>& pgn1,
  *         otherwise.
  * \pre `GpsTraits` must be a model of the concept `GeneralPolygonSetTraits_2`.
  * \pre `%ArrTraits` must be a model of the concept
- *      `ArrangementDirectionalXMonotoneTraits_2`.
+ *      `AosDirectionalXMonotoneTraits_2`.
  */
 template <typename ArrTraits, typename GpsTraits>
 bool
@@ -1415,7 +1415,7 @@ OutputIterator intersection(const Polygon_with_holes_2<Kernel, Container>& pgn1,
  *             `General_polygon_with_holes_2<General_polygon_2<ArrTraits>>`.
  * \return the past-the-end iterator of the output container.
  * \pre `%ArrTraits` must be a model of the concept
- *      `ArrangementDirectionalXMonotoneTraits_2`.
+ *      `AosDirectionalXMonotoneTraits_2`.
  */
 template <typename ArrTraits, typename OutputIterator>
 OutputIterator intersection(const General_polygon_2<ArrTraits>& pgn1,
@@ -1431,7 +1431,7 @@ OutputIterator intersection(const General_polygon_2<ArrTraits>& pgn1,
  *             `General_polygon_with_holes_2<General_polygon_2<ArrTraits>>`.
  * \return the past-the-end iterator of the output container.
  * \pre `%ArrTraits` must be a model of the concept
- *      `ArrangementDirectionalXMonotoneTraits_2`.
+ *      `AosDirectionalXMonotoneTraits_2`.
  */
 template <typename ArrTraits, typename OutputIterator>
 OutputIterator
@@ -1448,7 +1448,7 @@ intersection(const General_polygon_with_holes_2<General_polygon_2<ArrTraits>>& p
  *             `General_polygon_with_holes_2<General_polygon_2<ArrTraits>>`.
  * \return the past-the-end iterator of the output container.
  * \pre `%ArrTraits` must be a model of the concept
- *      `ArrangementDirectionalXMonotoneTraits_2`.
+ *      `AosDirectionalXMonotoneTraits_2`.
  */
 template <typename ArrTraits, typename OutputIterator>
 OutputIterator
@@ -1672,7 +1672,7 @@ intersection(const Polygon_with_holes_2<Kernel, Container>& pgn1,
  * \param traits a traits object.
  * \return the past-the-end iterator of the output container.
  * \pre `%ArrTraits` must be a model of the concept
- *      `ArrangementDirectionalXMonotoneTraits_2`.
+ *      `AosDirectionalXMonotoneTraits_2`.
  * \pre GpsTraits must be a model of `GeneralPolygonSetTraits_2`.
  */
 template <typename ArrTraits, typename OutputIterator, typename GpsTraits>
@@ -1693,7 +1693,7 @@ OutputIterator intersection(const General_polygon_2<ArrTraits>& pgn1,
  * \param traits a traits object.
  * \return the past-the-end iterator of the output container.
  * \pre `%ArrTraits` must be a model of the concept
- *      `ArrangementDirectionalXMonotoneTraits_2`.
+ *      `AosDirectionalXMonotoneTraits_2`.
  * \pre GpsTraits must be a model of `GeneralPolygonSetTraits_2`.
  */
 template <typename ArrTraits, typename OutputIterator, typename GpsTraits>
@@ -1715,7 +1715,7 @@ intersection(const General_polygon_with_holes_2<General_polygon_2<ArrTraits>>& p
  * \param traits a traits object.
  * \return the past-the-end iterator of the output container.
  * \pre `%ArrTraits` must be a model of the concept
- *      `ArrangementDirectionalXMonotoneTraits_2`.
+ *      `AosDirectionalXMonotoneTraits_2`.
  * \pre GpsTraits must be a model of `GeneralPolygonSetTraits_2`.
  */
 template <typename ArrTraits, typename OutputIterator, typename GpsTraits>
@@ -2026,7 +2026,7 @@ bool join(const Polygon_with_holes_2<Kernel, Container>& pgn1,
  * \param res the resulting union of \p pgn1 and \p pgn2.
  * \return `true` if the two input polygons overlap.
  * \pre `%ArrTraits` must be a model of the concept
- *      `ArrangementDirectionalXMonotoneTraits_2`.
+ *      `AosDirectionalXMonotoneTraits_2`.
  */
 template <typename ArrTraits>
 bool join(const General_polygon_2<ArrTraits>& pgn1,
@@ -2039,7 +2039,7 @@ bool join(const General_polygon_2<ArrTraits>& pgn1,
  * \param res the resulting union of \p pgn1 and \p pgn2.
  * \return `true` if the two input polygons overlap.
  * \pre `%ArrTraits` must be a model of the concept
- *      `ArrangementDirectionalXMonotoneTraits_2`.
+ *      `AosDirectionalXMonotoneTraits_2`.
  */
 template <typename ArrTraits>
 bool
@@ -2053,7 +2053,7 @@ join(const General_polygon_2<ArrTraits>& pgn1,
  * \param res the resulting union of \p pgn1 and \p pgn2.
  * \return `true` if the two input polygons overlap.
  * \pre `%ArrTraits` must be a model of the concept
- *      `ArrangementDirectionalXMonotoneTraits_2`.
+ *      `AosDirectionalXMonotoneTraits_2`.
  */
 template <typename ArrTraits>
 bool
@@ -2217,7 +2217,7 @@ bool join(const Polygon_with_holes_2<Kernel, Container>& pgn2,
  * \param traits a traits object.
  * \return `true` if the two input polygons overlap.
  * \pre `%ArrTraits` must be a model of the concept
- *      `ArrangementDirectionalXMonotoneTraits_2`.
+ *      `AosDirectionalXMonotoneTraits_2`.
  * \pre `GpsTraits` must be a model of the concept `GeneralPolygonSetTraits_2`.
  */
 template <typename ArrTraits, typename GpsTraits>
@@ -2234,7 +2234,7 @@ bool join(const General_polygon_2<ArrTraits>& pgn1,
  * \param traits a traits object.
  * \return `true` if the two input polygons overlap.
  * \pre `%ArrTraits` must be a model of the concept
- *      `ArrangementDirectionalXMonotoneTraits_2`.
+ *      `AosDirectionalXMonotoneTraits_2`.
  * \pre `GpsTraits` must be a model of the concept `GeneralPolygonSetTraits_2`.
  */
 template <typename ArrTraits, typename GpsTraits>
@@ -2252,7 +2252,7 @@ join(const General_polygon_2<ArrTraits>& pgn1,
  * \param traits a traits object.
  * \return `true` if the two input polygons overlap.
  * \pre `%ArrTraits` must be a model of the concept
- *      `ArrangementDirectionalXMonotoneTraits_2`.
+ *      `AosDirectionalXMonotoneTraits_2`.
  * \pre `GpsTraits` must be a model of the concept `GeneralPolygonSetTraits_2`.
  */
 template <typename ArrTraits, typename GpsTraits>
@@ -2568,7 +2568,7 @@ oriented_side(const Polygon_with_holes_2<Kernel, Container>& pgn1,
  * \param pgn1 1st the input polygon.
  * \param pgn2 the 2nd input polygon.
  * \pre `%ArrTraits` must be a model of the concept
- *      `ArrangementDirectionalXMonotoneTraits_2`.
+ *      `AosDirectionalXMonotoneTraits_2`.
  */
 template <typename ArrTraits>
 Oriented_side oriented_side(const General_polygon_2<ArrTraits>& pgn1,
@@ -2578,7 +2578,7 @@ Oriented_side oriented_side(const General_polygon_2<ArrTraits>& pgn1,
  * \param pgn1 the 1st input polygon.
  * \param pgn2 the 2nd input polygon.
  * \pre `%ArrTraits` must be a model of the concept
- *      `ArrangementDirectionalXMonotoneTraits_2`.
+ *      `AosDirectionalXMonotoneTraits_2`.
  */
 template <typename ArrTraits>
 Oriented_side
@@ -2589,7 +2589,7 @@ oriented_side(const General_polygon_2<ArrTraits>& pgn1,
  * \param pgn1 the 1st input polygon.
  * \param pgn2 the 2nd input polygon.
  * \pre `%ArrTraits` must be a model of the concept
- *      `ArrangementDirectionalXMonotoneTraits_2`.
+ *      `AosDirectionalXMonotoneTraits_2`.
  */
 template <typename ArrTraits>
 Oriented_side
@@ -2655,7 +2655,7 @@ Oriented_side oriented_side(const Polygon_with_holes_2<Kernel, Container>& pgn1,
  * \param pgn2 the 2nd input polygon.
  * \param traits a traits object.
  * \pre `%ArrTraits` must be a model of the concept
- *      `ArrangementDirectionalXMonotoneTraits_2`.
+ *      `AosDirectionalXMonotoneTraits_2`.
  * \pre `GpsTraits` must be a model of the concept `GeneralPolygonSetTraits_2`.
  *
  */
@@ -2669,7 +2669,7 @@ Oriented_side oriented_side(const General_polygon_2<ArrTraits>& pgn1,
  * \param pgn2 the 2nd input polygon.
  * \param traits a traits object.
  * \pre `%ArrTraits` must be a model of the concept
- *      `ArrangementDirectionalXMonotoneTraits_2`.
+ *      `AosDirectionalXMonotoneTraits_2`.
  * \pre `GpsTraits` must be a model of the concept `GeneralPolygonSetTraits_2`.
  *
  */
@@ -2684,7 +2684,7 @@ oriented_side(const General_polygon_2<ArrTraits>& pgn1,
  * \param pgn2 the 2nd input polygon.
  * \param traits a traits object.
  * \pre `%ArrTraits` must be a model of the concept
- *      `ArrangementDirectionalXMonotoneTraits_2`.
+ *      `AosDirectionalXMonotoneTraits_2`.
  * \pre `GpsTraits` must be a model of the concept `GeneralPolygonSetTraits_2`.
  *
  */
@@ -2727,7 +2727,7 @@ Oriented_side oriented_side(const Point_2& p,
  * \param p the input point.
  * \param pgn the input polygon.
  * \pre `%ArrTraits` must be a model of the concept
- *      `ArrangementDirectionalXMonotoneTraits_2`.
+ *      `AosDirectionalXMonotoneTraits_2`.
  */
 template <typename ArrTraits>
 Oriented_side oriented_side(const Point_2& p,
@@ -2770,7 +2770,7 @@ Oriented_side oriented_side(const Point_2& p,
  * \param pgn the input polygon.
  * \param traits a traits object.
  * \pre `%ArrTraits` must be a model of the concept
- *      `ArrangementDirectionalXMonotoneTraits_2`.
+ *      `AosDirectionalXMonotoneTraits_2`.
  * \pre `GpsTraits` must be a model of the concept `GeneralPolygonSetTraits_2`.
  */
 template <typename ArrTraits, typename GpsTraits>
@@ -3063,7 +3063,7 @@ symmetric_difference(const Polygon_with_holes_2<Kernel, Container>& pgn1,
  *             `General_polygon_with_holes_2<General_polygon_2<ArrTraits>>`.
  * \return the past-the-end iterator of the output container.
  * \pre `%ArrTraits` must be a model of the concept
- *      `ArrangementDirectionalXMonotoneTraits_2`.
+ *      `AosDirectionalXMonotoneTraits_2`.
  */
 template <typename ArrTraits, typename OutputIterator>
 OutputIterator symmetric_difference(const General_polygon_2<ArrTraits>& pgn1,
@@ -3081,7 +3081,7 @@ OutputIterator symmetric_difference(const General_polygon_2<ArrTraits>& pgn1,
  *             `General_polygon_with_holes_2<General_polygon_2<ArrTraits>>`.
  * \return the past-the-end iterator of the output container.
  * \pre `%ArrTraits` must be a model of the concept
- *      `ArrangementDirectionalXMonotoneTraits_2`.
+ *      `AosDirectionalXMonotoneTraits_2`.
  */
 template <typename ArrTraits, typename OutputIterator>
 OutputIterator
@@ -3100,7 +3100,7 @@ symmetric_difference(const General_polygon_with_holes_2<General_polygon_2<ArrTra
  *             `General_polygon_with_holes_2<General_polygon_2<ArrTraits>>`.
  * \return the past-the-end iterator of the output container.
  * \pre `%ArrTraits` must be a model of the concept
- *      `ArrangementDirectionalXMonotoneTraits_2`.
+ *      `AosDirectionalXMonotoneTraits_2`.
  */
 template <typename ArrTraits, typename OutputIterator>
 OutputIterator
@@ -3332,7 +3332,7 @@ symmetric_difference(const Polygon_with_holes_2<Kernel, Container>& pgn1,
  * \param traits a traits object.
  * \return the past-the-end iterator of the output container.
  * \pre `%ArrTraits` must be a model of the concept
- *      `ArrangementDirectionalXMonotoneTraits_2`.
+ *      `AosDirectionalXMonotoneTraits_2`.
  * \pre GpsTraits must be a model of `GeneralPolygonSetTraits_2`.
  */
 template <typename ArrTraits, typename OutputIterator, typename GpsTraits>
@@ -3353,7 +3353,7 @@ OutputIterator symmetric_difference(const General_polygon_2<ArrTraits>& pgn1,
  * \param traits a traits object.
  * \return the past-the-end iterator of the output container.
  * \pre `%ArrTraits` must be a model of the concept
- *      `ArrangementDirectionalXMonotoneTraits_2`.
+ *      `AosDirectionalXMonotoneTraits_2`.
  * \pre GpsTraits must be a model of `GeneralPolygonSetTraits_2`.
  */
 template <typename ArrTraits, typename OutputIterator, typename GpsTraits>
@@ -3375,7 +3375,7 @@ symmetric_difference(const General_polygon_with_holes_2<General_polygon_2<ArrTra
  * \param traits a traits object.
  * \return the past-the-end iterator of the output container.
  * \pre `%ArrTraits` must be a model of the concept
- *      `ArrangementDirectionalXMonotoneTraits_2`.
+ *      `AosDirectionalXMonotoneTraits_2`.
  * \pre GpsTraits must be a model of `GeneralPolygonSetTraits_2`.
  */
 template <typename ArrTraits, typename OutputIterator, typename GpsTraits>
diff --git a/Boolean_set_operations_2/doc/Boolean_set_operations_2/CGAL/General_polygon_2.h b/Boolean_set_operations_2/doc/Boolean_set_operations_2/CGAL/General_polygon_2.h
index c5c628cc757..ac8899ed76e 100644
--- a/Boolean_set_operations_2/doc/Boolean_set_operations_2/CGAL/General_polygon_2.h
+++ b/Boolean_set_operations_2/doc/Boolean_set_operations_2/CGAL/General_polygon_2.h
@@ -7,10 +7,10 @@ namespace CGAL {
 The class `General_polygon_2` models the concept `GeneralPolygon_2`.
 It represents a simple general-polygon. It is parameterized with the type
 `ArrTraits` that models the concept
-`ArrangementDirectionalXMonotoneTraits_2`. The latter is a refinement
-of the concept `ArrangementXMonotoneTraits_2`. In addition to the
-requirements of the concept `ArrangementXMonotoneTraits_2`, a
-model of the concept `ArrangementDirectionalXMonotoneTraits_2` must
+`AosDirectionalXMonotoneTraits_2`. The latter is a refinement
+of the concept `AosXMonotoneTraits_2`. In addition to the
+requirements of the concept `AosXMonotoneTraits_2`, a
+model of the concept `AosDirectionalXMonotoneTraits_2` must
 support the following functions:
 <UL>
 <LI>Given an \f$ x\f$-monotone curve, construct its opposite curve.
diff --git a/Boolean_set_operations_2/doc/Boolean_set_operations_2/CGAL/General_polygon_set_2.h b/Boolean_set_operations_2/doc/Boolean_set_operations_2/CGAL/General_polygon_set_2.h
index 7490789ba66..f65b5d11004 100644
--- a/Boolean_set_operations_2/doc/Boolean_set_operations_2/CGAL/General_polygon_set_2.h
+++ b/Boolean_set_operations_2/doc/Boolean_set_operations_2/CGAL/General_polygon_set_2.h
@@ -50,7 +50,7 @@ boundary and the holes are also pairwise disjoint, except perhaps at the
 vertices.
 
 \sa `Arrangement_2`
-\sa `ArrangementXMonotoneTraits_2`
+\sa `AosXMonotoneTraits_2`
 \sa `Nef_polyhedron_2`
 
 */
diff --git a/Boolean_set_operations_2/doc/Boolean_set_operations_2/CGAL/Gps_traits_2.h b/Boolean_set_operations_2/doc/Boolean_set_operations_2/CGAL/Gps_traits_2.h
index 6d65a9e5e43..ca47397e6a2 100644
--- a/Boolean_set_operations_2/doc/Boolean_set_operations_2/CGAL/Gps_traits_2.h
+++ b/Boolean_set_operations_2/doc/Boolean_set_operations_2/CGAL/Gps_traits_2.h
@@ -7,8 +7,8 @@ namespace CGAL {
 The traits class `Gps_traits_2` models the concept
 `GeneralPolygonSetTraits_2`. It inherits from the instantiated
 type of the template parameter `ArrTraits`, which must model the
-concept `ArrangementDirectionalXMonotoneTraits_2`, (which in turn refines
-the concept `ArrangementXMonotoneTraits_2`). The template parameter
+concept `AosDirectionalXMonotoneTraits_2`, (which in turn refines
+the concept `AosXMonotoneTraits_2`). The template parameter
 `GeneralPolygon_t` must be instantiated with a model of the concept
 of `GpsTraitsGeneralPolygon_2`. By default, the latter is instantiated by
 `CGAL::General_polygon_2<ArrTraits>`.
diff --git a/Boolean_set_operations_2/doc/Boolean_set_operations_2/Concepts/ArrangementDirectionalXMonotoneTraits_2.h b/Boolean_set_operations_2/doc/Boolean_set_operations_2/Concepts/AosDirectionalXMonotoneTraits_2.h
similarity index 80%
rename from Boolean_set_operations_2/doc/Boolean_set_operations_2/Concepts/ArrangementDirectionalXMonotoneTraits_2.h
rename to Boolean_set_operations_2/doc/Boolean_set_operations_2/Concepts/AosDirectionalXMonotoneTraits_2.h
index 3278e482000..1f2e9dac658 100644
--- a/Boolean_set_operations_2/doc/Boolean_set_operations_2/Concepts/ArrangementDirectionalXMonotoneTraits_2.h
+++ b/Boolean_set_operations_2/doc/Boolean_set_operations_2/Concepts/AosDirectionalXMonotoneTraits_2.h
@@ -7,14 +7,14 @@ This concept refines the basic arrangement \f$ x\f$-monotone traits concept.
 A model of this concept is able to handle <I>directed</I> \f$ x\f$-monotone curves
 that intersect in their interior. Namely, an instance of the
 `X_monotone_curve_2` type defined by a model of the concept
-`ArrangementXMonotoneTraits_2` is only required to have a <I>left</I>
+`AosXMonotoneTraits_2` is only required to have a <I>left</I>
 (lexicographically smaller) endpoint and a <I>right</I> endpoint.
 If the traits class is also a model of
-`ArrangementDirectionalXMonotoneTraits_2`, the \f$ x\f$-monotone curve is
+`AosDirectionalXMonotoneTraits_2`, the \f$ x\f$-monotone curve is
 also required to have a direction, namely one of these two endpoint serves
 as its <I>source</I> and the other as its <I>target</I>.
 
-\cgalRefines{ArrangementXMonotoneTraits_2}
+\cgalRefines{AosXMonotoneTraits_2}
 
 \cgalHasModelsBegin
 \cgalHasModels{CGAL::Arr_segment_traits_2<Kernel>}
@@ -26,11 +26,11 @@ as its <I>source</I> and the other as its <I>target</I>.
 \cgalHasModels{CGAL::Arr_algebraic_segment_traits_2<Coefficient>}
 \cgalHasModelsEnd
 
-\sa `ArrangementXMonotoneTraits_2`
+\sa `AosXMonotoneTraits_2`
 
 */
 
-class ArrangementDirectionalXMonotoneTraits_2 {
+class AosDirectionalXMonotoneTraits_2 {
 public:
 
 /// \name Functor Types
@@ -74,17 +74,17 @@ typedef unspecified_type Merge_2;
 /*!
 default constructor.
 */
-ArrangementDirectionalXMonotoneTraits_2();
+AosDirectionalXMonotoneTraits_2();
 
 /*!
 copy constructor
 */
-ArrangementDirectionalXMonotoneTraits_2(ArrangementDirectionalXMonotoneTraits_2 other);
+AosDirectionalXMonotoneTraits_2(AosDirectionalXMonotoneTraits_2 other);
 
 /*!
 assignment operator.
 */
-ArrangementDirectionalXMonotoneTraits_2 operator=(other);
+AosDirectionalXMonotoneTraits_2 operator=(other);
 
 /// @}
 
@@ -103,5 +103,4 @@ Construct_opposite_2 construct_opposite_2_object();
 
 /// @}
 
-}; /* end ArrangementDirectionalXMonotoneTraits_2 */
-
+}; /* end AosDirectionalXMonotoneTraits_2 */
diff --git a/Boolean_set_operations_2/doc/Boolean_set_operations_2/Concepts/ArrDirectionalTraits--AreMergeable_2.h b/Boolean_set_operations_2/doc/Boolean_set_operations_2/Concepts/ArrDirectionalTraits--AreMergeable_2.h
index 65fd4f347a8..93f15a825bf 100644
--- a/Boolean_set_operations_2/doc/Boolean_set_operations_2/Concepts/ArrDirectionalTraits--AreMergeable_2.h
+++ b/Boolean_set_operations_2/doc/Boolean_set_operations_2/Concepts/ArrDirectionalTraits--AreMergeable_2.h
@@ -6,7 +6,7 @@ namespace ArrDirectionalTraits {
 \cgalRefines{AdaptableBinaryFunction}
 
 \cgalHasModelsBegin
-\cgalHasModels{ArrangementDirectionalXMonotoneTraits_2::Are_mergeable_2}
+\cgalHasModels{AosDirectionalXMonotoneTraits_2::Are_mergeable_2}
 \cgalHasModelsEnd
 
 */
diff --git a/Boolean_set_operations_2/doc/Boolean_set_operations_2/Concepts/ArrDirectionalTraits--CompareEndpointsXy_2.h b/Boolean_set_operations_2/doc/Boolean_set_operations_2/Concepts/ArrDirectionalTraits--CompareEndpointsXy_2.h
index e7714c04561..daf5b7a705c 100644
--- a/Boolean_set_operations_2/doc/Boolean_set_operations_2/Concepts/ArrDirectionalTraits--CompareEndpointsXy_2.h
+++ b/Boolean_set_operations_2/doc/Boolean_set_operations_2/Concepts/ArrDirectionalTraits--CompareEndpointsXy_2.h
@@ -7,7 +7,7 @@ namespace ArrDirectionalTraits {
 \cgalRefines{AdaptableUnaryFunction}
 
 \cgalHasModelsBegin
-\cgalHasModels{ArrangementDirectionalXMonotoneTraits_2::Compare_endpoints_xy_2}
+\cgalHasModels{AosDirectionalXMonotoneTraits_2::Compare_endpoints_xy_2}
 \cgalHasModelsEnd
 
 */
diff --git a/Boolean_set_operations_2/doc/Boolean_set_operations_2/Concepts/ArrDirectionalTraits--ConstructOpposite_2.h b/Boolean_set_operations_2/doc/Boolean_set_operations_2/Concepts/ArrDirectionalTraits--ConstructOpposite_2.h
index 92ee2585b2d..c61205872cb 100644
--- a/Boolean_set_operations_2/doc/Boolean_set_operations_2/Concepts/ArrDirectionalTraits--ConstructOpposite_2.h
+++ b/Boolean_set_operations_2/doc/Boolean_set_operations_2/Concepts/ArrDirectionalTraits--ConstructOpposite_2.h
@@ -7,7 +7,7 @@ namespace ArrDirectionalTraits {
 \cgalRefines{AdaptableUnaryFunction}
 
 \cgalHasModelsBegin
-\cgalHasModels{ArrangementDirectionalXMonotoneTraits_2::Construct_opposite_2}
+\cgalHasModels{AosDirectionalXMonotoneTraits_2::Construct_opposite_2}
 \cgalHasModelsEnd
 
 */
diff --git a/Boolean_set_operations_2/doc/Boolean_set_operations_2/Concepts/ArrDirectionalTraits--Intersect_2.h b/Boolean_set_operations_2/doc/Boolean_set_operations_2/Concepts/ArrDirectionalTraits--Intersect_2.h
index 35c4fdf3273..4b6fcea1cc0 100644
--- a/Boolean_set_operations_2/doc/Boolean_set_operations_2/Concepts/ArrDirectionalTraits--Intersect_2.h
+++ b/Boolean_set_operations_2/doc/Boolean_set_operations_2/Concepts/ArrDirectionalTraits--Intersect_2.h
@@ -6,7 +6,7 @@ namespace ArrDirectionalTraits {
 \cgalRefines{AdaptableBinaryFunction}
 
 \cgalHasModelsBegin
-\cgalHasModels{ArrangementDirectionalXMonotoneTraits_2::Intersect_2}
+\cgalHasModels{AosDirectionalXMonotoneTraits_2::Intersect_2}
 \cgalHasModelsEnd
 
 */
diff --git a/Boolean_set_operations_2/doc/Boolean_set_operations_2/Concepts/ArrDirectionalTraits--Merge_2.h b/Boolean_set_operations_2/doc/Boolean_set_operations_2/Concepts/ArrDirectionalTraits--Merge_2.h
index 18f8f26e936..fa931a25d70 100644
--- a/Boolean_set_operations_2/doc/Boolean_set_operations_2/Concepts/ArrDirectionalTraits--Merge_2.h
+++ b/Boolean_set_operations_2/doc/Boolean_set_operations_2/Concepts/ArrDirectionalTraits--Merge_2.h
@@ -6,7 +6,7 @@ namespace ArrDirectionalTraits {
 \cgalRefines{AdaptableBinaryFunction}
 
 \cgalHasModelsBegin
-\cgalHasModels{ArrangementDirectionalXMonotoneTraits_2::Merge_2}
+\cgalHasModels{AosDirectionalXMonotoneTraits_2::Merge_2}
 \cgalHasModelsEnd
 
 */
diff --git a/Boolean_set_operations_2/doc/Boolean_set_operations_2/Concepts/ArrDirectionalTraits--Split_2.h b/Boolean_set_operations_2/doc/Boolean_set_operations_2/Concepts/ArrDirectionalTraits--Split_2.h
index 5d6529d4862..8cb1a811b3f 100644
--- a/Boolean_set_operations_2/doc/Boolean_set_operations_2/Concepts/ArrDirectionalTraits--Split_2.h
+++ b/Boolean_set_operations_2/doc/Boolean_set_operations_2/Concepts/ArrDirectionalTraits--Split_2.h
@@ -6,7 +6,7 @@ namespace ArrDirectionalTraits {
 \cgalRefines{AdaptableUnaryFunction}
 
 \cgalHasModelsBegin
-\cgalHasModels{ArrangementDirectionalXMonotoneTraits_2::Split_2}
+\cgalHasModels{AosDirectionalXMonotoneTraits_2::Split_2}
 \cgalHasModelsEnd
 
 */
diff --git a/Boolean_set_operations_2/doc/Boolean_set_operations_2/Concepts/GeneralPolygonSetDcel.h b/Boolean_set_operations_2/doc/Boolean_set_operations_2/Concepts/GeneralPolygonSetDcel.h
index 6d28d6afbf4..2df5a74cbda 100644
--- a/Boolean_set_operations_2/doc/Boolean_set_operations_2/Concepts/GeneralPolygonSetDcel.h
+++ b/Boolean_set_operations_2/doc/Boolean_set_operations_2/Concepts/GeneralPolygonSetDcel.h
@@ -9,12 +9,12 @@ It maintains the incidence relation among them. The halfedges are ordered
 in pairs sometimes referred to as twins, such that each halfedge pair
 represent an edge.
 
-A model of the `GeneralPolygonSetDcel` simply refines `ArrangementDcel`,
+A model of the `GeneralPolygonSetDcel` simply refines `AosDcel`,
 the `Halfedge` and `Face` types being models of the concepts
 `GeneralPolygonSetDcelHalfedge` and `GeneralPolygonSetDcelFace`
 respectively
 
-\cgalRefines{ArrangementDcel}
+\cgalRefines{AosDcel}
 
 \cgalHasModelsBegin
 \cgalHasModels{CGAL::Gps_default_dcel<Traits>}
@@ -28,4 +28,3 @@ respectively
 class GeneralPolygonSetDcel {};
 
 /* end GeneralPolygonSetDcel */
-
diff --git a/Boolean_set_operations_2/doc/Boolean_set_operations_2/Concepts/GeneralPolygonSetDcelFace.h b/Boolean_set_operations_2/doc/Boolean_set_operations_2/Concepts/GeneralPolygonSetDcelFace.h
index 01a99bce20e..5201673abe7 100644
--- a/Boolean_set_operations_2/doc/Boolean_set_operations_2/Concepts/GeneralPolygonSetDcelFace.h
+++ b/Boolean_set_operations_2/doc/Boolean_set_operations_2/Concepts/GeneralPolygonSetDcelFace.h
@@ -7,14 +7,14 @@ A face record in a \em Dcel data structure used by the
 `General_polygon_set_2` and `Polygon_set_2` template classes
 to represent the underlying internal `Arrangement_2` data structure.
 
-\cgalRefines{ArrangementDcelFace}
+\cgalRefines{AosDcelFace}
 
 \cgalHasModelsBegin
 \cgalHasModels{CGAL::Gps_face_base}
 \cgalHasModelsEnd
 
-\sa `ArrangementDcel`
-\sa `ArrangementDcelVertex`
+\sa `AosDcel`
+\sa `AosDcelVertex`
 \sa `GeneralPolygonSetDcelHalfedge`
 
 */
diff --git a/Boolean_set_operations_2/doc/Boolean_set_operations_2/Concepts/GeneralPolygonSetDcelHalfedge.h b/Boolean_set_operations_2/doc/Boolean_set_operations_2/Concepts/GeneralPolygonSetDcelHalfedge.h
index a21a5fd8b7f..975fc355f4c 100644
--- a/Boolean_set_operations_2/doc/Boolean_set_operations_2/Concepts/GeneralPolygonSetDcelHalfedge.h
+++ b/Boolean_set_operations_2/doc/Boolean_set_operations_2/Concepts/GeneralPolygonSetDcelHalfedge.h
@@ -6,14 +6,14 @@ A halfedge record in a \em Dcel data structure used
 by the `General_polygon_set_2` and `Polygon_set_2` template classes
 to represent the underlying internal `Arrangement_2` data structure.
 
-\cgalRefines{ArrangementDcelHalfedge}
+\cgalRefines{AosDcelHalfedge}
 
 \cgalHasModelsBegin
 \cgalHasModels{CGAL::Gps_face_halfedge}
 \cgalHasModelsEnd
 
-\sa `ArrangementDcel`
-\sa `ArrangementDcelVertex`
+\sa `AosDcel`
+\sa `AosDcelVertex`
 \sa `GeneralPolygonSetDcelFace`
 
 */
diff --git a/Boolean_set_operations_2/doc/Boolean_set_operations_2/Concepts/GeneralPolygonSetTraits_2.h b/Boolean_set_operations_2/doc/Boolean_set_operations_2/Concepts/GeneralPolygonSetTraits_2.h
index 2c8966d8239..a1c48bf7217 100644
--- a/Boolean_set_operations_2/doc/Boolean_set_operations_2/Concepts/GeneralPolygonSetTraits_2.h
+++ b/Boolean_set_operations_2/doc/Boolean_set_operations_2/Concepts/GeneralPolygonSetTraits_2.h
@@ -11,7 +11,7 @@ a type that represents a general polygon and another one that represents
 general polygon with holes. It also requires operations that operate on these
 types.
 
-\cgalRefines{ArrangementDirectionalXMonotoneTraits_2}
+\cgalRefines{AosDirectionalXMonotoneTraits_2}
 
 \cgalHasModelsBegin
 \cgalHasModels{CGAL::Gps_segment_traits_2<Kernel,Container,ArrSegmentTraits>}
@@ -19,7 +19,7 @@ types.
 \cgalHasModels{CGAL::Gps_traits_2<ArrTraits,GeneralPolygon>}
 \cgalHasModelsEnd
 
-\sa `ArrangementDirectionalXMonotoneTraits_2`
+\sa `AosDirectionalXMonotoneTraits_2`
 
 */
 
diff --git a/Boolean_set_operations_2/doc/Boolean_set_operations_2/PackageDescription.txt b/Boolean_set_operations_2/doc/Boolean_set_operations_2/PackageDescription.txt
index a562dd4e48a..9dca99e32af 100644
--- a/Boolean_set_operations_2/doc/Boolean_set_operations_2/PackageDescription.txt
+++ b/Boolean_set_operations_2/doc/Boolean_set_operations_2/PackageDescription.txt
@@ -42,7 +42,7 @@ containment predicates.
 - `GpsTraitsGeneralPolygon_2`
 - `GpsTraitsGeneralPolygonWithHoles_2`
 - `GeneralPolygon_2`
-- `ArrangementDirectionalXMonotoneTraits_2`
+- `AosDirectionalXMonotoneTraits_2`
 - `GeneralPolygonSetTraits_2`
 - `GeneralPolygonSetDcel`
 - `GeneralPolygonSetDcelFace`