  F-theory/heterotic duality is formulated in the stable degeneration limit of
a K3 fibration on the F-theory side. In this note, we analyze the structure of
the stable degeneration limit. We discuss whether stable degeneration exists
for pairs of rational elliptic surfaces. We demonstrate that, when two rational
elliptic surfaces have an identical complex structure, stable degeneration
always exists. We provide an equation that systematically describes the stable
degeneration of a K3 surface into a pair of isomorphic rational elliptic
surfaces. When two rational elliptic surfaces have different complex
structures, whether their sum glued along a smooth fiber admits deformation to
a K3 surface can be determined by studying the structure of the K3 lattice. We
investigate the lattice theoretic condition to determine whether a deformation
to a K3 surface exists for pairs of extremal rational elliptic surfaces. In
addition, we discuss the configurations of singular fibers under stable
degeneration. The sum of two isomorphic rational elliptic surfaces glued
together admits a deformation to a K3 surface, the singular fibers of which are
twice that of the rational elliptic surface. For special situations, singular
fibers of the resulting K3 surface collide and they are enhanced to a fiber of
another type. Some K3 surfaces become attractive in these situations. We
determine the complex structures and the Weierstrass forms of these attractive
K3 surfaces. We also deduce the gauge groups in F-theory compactifications on
these attractive K3 surfaces times a K3. $E_6$, $E_7$, $E_8$, $SU(5)$, and
$SO(10)$ gauge groups arise in these compactifications.
