  Interest in anti-unification, the dual problem of unification, is on the rise
due to applications within the field of software analysis and related areas.
For example, anti-unification-based techniques have found uses within clone
detection and automatic program repair methods. While syntactic forms of
anti-unification are enough for many applications, some aspects of software
analysis methods are more appropriately modeled by reasoning modulo an
equational theory. Thus, extending existing anti-unification methods to deal
with important equational theories is the natural step forward. This paper
considers anti-unification modulo pure absorption theories, i.e., some
operators are associated with a special constant satisfying the axiom
$f(x,\varepsilon_f) \approx f(\varepsilon_f,x) \approx \varepsilon_f$. We
provide a sound and complete rule-based algorithm for such theories.
Furthermore, we show that anti-unification modulo absorption is infinitary.
Despite this, our algorithm terminates and produces a finitary algorithmic
representation of the minimal complete set of solutions. We also show that the
linear variant is finitary.
