The transitivity conjecture for the Langlands-factor partial order

Let $G$ be a reductive algebraic group over a local field $F$. For irreducible admissible representations of $G(F)$, define $\pi_1\geq\pi_2$ when $\pi_1$ appears as a Jordan–Hölder factor of the standard module whose Langlands quotient is $\pi_2$. Transitivity conjecture. If $\pi_1\geq\pi_2$ and $\pi_2\geq\pi_3$, then $\pi_1\geq\pi_3$; equivalently, the relation is an equivalence relation.