Induction from two linked segments with one half border and cuspidal reducibility

In this paper, we determine the composition series of the induced representation $\delta ([{\nu }^{\frac{1}{2}}\rho ,{\nu }^c\rho ])\times \delta ([{\nu }^{-a}\rho ,{\nu }^b\rho ])⋊\sigma$ where $a,b,c\in \mathbb{Z}+\frac{1}{2}$ such that $\frac{1}{2}\le a<b<c$, $\rho$ is an irreducible cuspidal unitary representation of a general linear group and $\sigma$ is an irreducible cuspidal representation of a classical group such that ${\nu }^{\frac{1}{2}}\rho ⋊\sigma$ reduces.