Finiteness conjecture for chains of definable subgroups of abelian interpretable groups

Let $X$ be an abelian interpretable group. By Corollary~, there is an increasing chain of \textit{dfg} subgroups $(Y_i:i<\alpha)$ with $Y_0=0$, whose successive quotients have dp-rank $1$; when the chain terminates, the final quotient is definably compact and has \textit{fsg}. Finiteness conjecture. The ordinal $b1$ is finite. Therefore, any abelian interpretable group $X$ sits in a short exact sequence

$$1\to Y_{\alpha-1}\to X\to X/Y_{\alpha-1}\to 1,$$

where $Y_{\alpha-1}$ has \textit{dfg} and $X/Y_{\alpha-1}$ has \textit{fsg} and is definably compact. The conjecture is automatic for definable groups because the dimensions of the successive subgroups strictly increase, but it remains unclear for general interpretable groups.