  In this paper, we consider the reconfiguration problem of integer linear
systems. In this problem, we are given an integer linear system $I$ and two
feasible solutions $\boldsymbol{s}$ and $\boldsymbol{t}$ of $I$, and then asked
to transform $\boldsymbol{s}$ to $\boldsymbol{t}$ by changing a value of only
one variable at a time, while maintaining a feasible solution of $I$
throughout. $Z(I)$ for $I$ is the complexity index introduced by Kimura and
Makino (Discrete Applied Mathematics 200:67--78, 2016), which is defined by the
sign pattern of the input matrix. We analyze the complexity of the
reconfiguration problem of integer linear systems based on the complexity index
$Z(I)$ of given $I$. We then show that the problem is (i) solvable in constant
time if $Z(I)$ is less than one, (ii) weakly coNP-complete and
pseudo-polynomially solvable if $Z(I)$ is exactly one, and (iii)
PSPACE-complete if $Z(I)$ is greater than one. Since the complexity indices of
Horn and two-variable-par-inequality integer linear systems are at most one,
our results imply that the reconfiguration of these systems are in coNP and
pseudo-polynomially solvable. Moreover, this is the first result that reveals
coNP-completeness for a reconfiguration problem, to the best of our knowledge.
