The traits class Arr_non_caching_segment_basic_traits_2<Kernel> is a model of the ArrangementTraits_2 concept that allow the construction and maintenance of arrangements of sets of pairwise interior-disjoint line segments. It is templated with a CGAL-Kernel model, and it is derived from it. This traits class is a thin layer above the parameterized kernel. It inherits the Point_2 from the kernel and its X_monotone_curve_2 type is defined as Kernel::Segment_2. Most traits-class functor are inherited from the kernel functor, and the traits class only supplies the necessary functors that are not provided by the kernel. The kernel is parameterized with a number type, which should support the arithmetic operations , and in an exact manner in order to avoid robustness problems. Using Cartesian<MP_Float> or Cartesian<Gmpz> are possible instantiations for the kernel. Using other (inexact) number types (for example, instatiating the template with Simple_cartesian<double>) is also possible, at the user's own risk.