Cyclic Ramsey conjecture for alternating and reverse alternating paths

Let $P_a^\mathrm{alt}$ be an alternating path of order $a$ and $P_b^\mathrm{ralt}$ a reverse alternating path of order $b$. Alternating–reverse-alternating conjecture. For any $a, b \ge 2$, we have

$$R_\mathrm{cyc}(P_a^\mathrm{alt}, P_b^\mathrm{ralt}) = a + b - 2 - (ab \bmod 2).$$

The formula is suggested by the computed cyclic values, which appear to agree with those for two alternating paths. The general statement remains open.