are assumed to be complete lattices which are related by abstraction and concretization maps $\alpha:C{\rightarrow}A$ and $\gamma:A {\rightarrow}C$ that give rise to an adjunction $(\alpha,C,A,\gamma)$, that is, for all $a$ and $c$, $\alpha(c) \leq_A a {\Leftrightarrow}c \leq_C \gamma(a)$. It is known that $\ok{\mu_A {\triangleq}\gamma \circ \alpha: C {\rightarrow}C}$ is an upper closure operator (uco) on $C$, i.e. a monotone, idempotent and increasing function. Also, abstract domains can be equivalently defined as ucos, meaning that any GI $(\alpha,C,A,\gamma)$ induces the uco $\mu_A$, any uco $\mu: C{\rightarrow}C$ induces the GI $(\mu, C, \mu(C), \lambda x.x)$, and these two transforms are the inverse of each other. GIs of a common concrete domain $C$ are preordered w.r.t. their relative precision as usual: ${\mathcal{G}}_1 = (\alpha_1,C,A_1,\gamma_1)\sqsubseteq {\mathcal{G}}_2=(\alpha_2,C,A_2,\gamma_2)$ — i.e. $A_1$/$A_2$ is a refinement/simplification of $A_2$/$A_1$ — iff $\gamma_2 (\alpha_2(C)) \subseteq\gamma_1 (\alpha_1 (C))$. Moreover, ${\mathcal{G}}_1$ and ${\mathcal{G}}_2$ are equivalent when ${\mathcal{G}}_1
\sqsubseteq {\mathcal{G}}_2$ and ${\mathcal{G}}_2 \sqsubseteq {\mathcal{G}}_1$. We denote by $\operatorname{Abs}(C)$ the family of abstract domains of $C$ up to the above equivalence. It is well known that $\tuple{\operatorname{Abs}(C),\sqsubseteq}$ is a complete lattice, so that one can consider the most concrete simplification (i.e., lub $\sqcup$) and the most abstract refinement (i.e., glb $\sqcap$) of any family 