Comparative evolution of the properties of the inner binary of the triple with and without a third star. The three panels, from top to bottom, display the zoomed-in evolution of key parameters of the two stars: eccentricity, semi-major axis, and radius. In the case of the triple system, the inner binary experiences unstable mass transfer, causing it to shrink further and eventually enter the LISA band. Meanwhile, the inner binary when evolved without a tertiary star undergoes mass loss due to winds, resulting in an increase in its semi-major axis and a widening of the orbit. Here a₁ (triple) and e₁ (triple) represent the semi-major axis and eccentricity of the inner binary evolved with a tertiary star, while a (binary) and e (binary) show the semi-major axis and eccentricity of the same inner binary evolved without the tertiary star. Additionally, r₁ and r₂ represent the radii of the primary and secondary stars in the inner binary, respectively.