  The Taylor expansion, which stems from Linear Logic and its differential
extensions, is an approximation framework for the $\lambda$-calculus (and many
of its variants). The reduction of the approximants of a $\lambda$-term induces
a reduction on the $\lambda$-term itself, which enjoys a simulation property:
whenever a term reduces to another, the approximants reduce accordingly. In
recent work, we extended this result to an infinitary $\lambda$-calculus
(namely, $\Lambda_{\infty}^{001}$). This short paper solves the question
whether the converse property also holds: if the approximants of some term
reduce to the approximants of another term, is there a $\beta$-reduction
between these terms? This happens to be true for the $\lambda$-calculus, as we
show, but our proof fails in the infinitary case. We exhibit a counter-example,
refuting the conservativity for $\Lambda_{\infty}^{001}$.
