$$
\end{definition}
+\section{Coalescing}\label{s:coalescing}
+
+See \shortciteN{Verdoolaege2009isl}, for now.
+More details will be added later.
+
\section{Transitive Closure}
\subsection{Introduction}
any offsets from one or more $\Delta_i'$.
The path that consists of only identity relations is removed
by imposing the constraint $y_{d+1} - x_{d+1} > 0$.
+Taking the union with the identity relation means that
+that the relations we compose in \eqref{eq:transitive:decompose}
+each consist of two basic relations. If there are $m$
+disjuncts in the input relation, then a direct application
+of the composition operation may therefore result in a relation
+with $2^m$ disjuncts, which is prohibitively expensive.
+It is therefore crucial to apply coalescing (\autoref{s:coalescing})
+after each composition.
Let us now consider how to compute an overapproximation of $P_i'$.
Those that correspond to singleton $\Delta_i$s are grouped together
institution = "University of Maryland",
year = 1996
}
+
+@unpublished{Verdoolaege2009isl,
+ author = "Verdoolaege, Sven",
+ title = "An integer set library for program analysis",
+ note = "Advances in the Theory of Integer Linear Optimization and its Extensions,AMS 2009 Spring Western Section Meeting, San Francisco, California, 25-26 April 2009",
+ month = Apr,
+ year = "2009",
+ url = "https://lirias.kuleuven.be/handle/123456789/228373",
+}
if (j < d) {
path = isl_map_apply_range(path,
path_along_delta(isl_dim_copy(dim), delta));
+ path = isl_map_coalesce(path);
} else {
isl_basic_set_free(delta);
++n;