Conjecture on $t_3$ and $\bar t_4$ moves to trivial links

Let a link be $t_3$, $\bar t_4$ equivalent to another link when it can be obtained from it by $t_3$ and $\bar t_4$ moves and isotopy. The $t_3$–$\bar t_4$ trivial-link conjecture. Every link is $t_3$, $\bar t_4$ equivalent to a trivial link. The source presents this as a conjecture but gives no resolution or counterexample, so its status remains open.