We use the notion of the gauge/string duality and discuss the Liouvillian (non) integrability criteria for string sigma models in the context of recently proposed Arutyunov-Bassi-Lacroix (ABL) model in Arutyunov et al. (2021) . Our analysis complements those previous results due to numerical analysis as well as Lax pair formulation. We consider a winding string ansatz for the deformed torus Tk (λ1 ,λ2 , λ) which can be interpreted as a system of coupled pendulums. Our analysis reveals the Liouvillian nonintegrability of the associated sigma model. We also obtain the generalized decoupling limit and confirm the analytic integrability for the decoupled sector.