is a contradiction. Thus, by [@Rogozin68], $0$ is regular for half-lines $(-\infty,0)$ and $(0,\infty)$. Now, let $\mathbf{L}=(L_t\colon t {\geqslant}0)$ be a local time at $0$ for the process $\mathbf{S}-\mathbf{X}$, where $S_t = \sup_{s {\leqslant}t}X_s$, and $\mathbf{L}^{-1}$ — its right-continuous inverse, called *the ascending ladder time process*. Next, we define $\mathbf{H}$ by setting $H_t = S_{L^{-1}_t}=X_{L^{-1}_t}$ on $\{ L^{-1}_t<\infty \}$ and $H_t=\infty$ otherwise. $\mathbf{H}$ is a (possibly killed) subordinator called *the ascending ladder height process*.

Next, we introduce the renewal function $V$ as a potential measure of the interval $[0,x]$ for the ascending ladder height process, i.e. $V(x) = \int_0^{\infty} {\mathbb{P}}(H_s {\leqslant}x)\,ds$, with the convention $V(x)=0$ for $x < 0$. Similarly, $\widehat{V}(x) = \int_0^{\infty} {\mathbb{P}}(\widehat{H}_s {\leqslant}x)\,ds$ and $\widehat{V}(x)=0$ for $x < 0$. Clearly, if $\mathbf{X}$ is symmetric, then $\widehat{\mathbf{X}} = \mathbf{X}$ and consequently, $\widehat{V}=V$. Directly from the definition of $V$ and $\widehat{V}$ we conclude that both are subadditive. Moreover, by [@Silverstein80 Theorem 1 and 2], $\widehat{V}$ and $\widehat{V}'$ are harmonic on $(0,\infty)$, but $V$ and $V'$ are coharmonic on $(0,\infty)$. In fact, also from [@Silverstein80] we have that both $V'$ and $\widehat{V}'$ are positive on $(0,\infty)$, hence both $V$ and $\widehat{V}$ are actually strictly increasing on $(0,\infty)$. One feature that will 