  We study the consistency of the decoupling limit of the generalized SU(2)
Proca theory (GSU2P). Namely, we study the healthiness of those terms whose
analysis in the scalar limit was not originally established in the
reconstruction of the full theory (see the work by Gallego Cadavid et. al.
[Phys. Rev. D 102, 104066 (2020)]). Those terms are the parity-violating
$\tilde{\mathcal{L}}_{4,2}^1$ and the parity-conserving beyond SU(2) Proca
terms $\mathcal{L}_{4,2}^3$ and $\mathcal{L}_{4,2}^4$. Using the 3+1
Arnowitt-Deser-Misner formalism, we write down the kinetic Lagrangian of these
terms in the decoupling limit and show that their corresponding kinetic
matrices are degenerate. This degeneracy is a necessary condition for the
propagation of the right number of degrees of freedom, as required by the
primary constraint-enforcing relation. Interestingly, the
$\tilde{\mathcal{L}}_{4,2}^1$ term, which is purely non-Abelian, does not
contribute to the kinetic Lagrangian of the theory, so its contribution is
trivially degenerate. Similarly, but not trivially in these cases, the
contributions of the $\mathcal{L}_{4,2}^3$ and $\mathcal{L}_{4,2}^4$ terms to
the kinetic Lagrangian turn out to be degenerate as well. The results presented
in this paper represent progress in the construction of the fully healthy
GSU2P.
