Unbounded hardness conjecture for unknot diagrams

Let $m$ be an integer and let $\hat{\mathcal{D}}$ be the $0$-crossing diagram of the unknot. A diagram of the unknot $\mathcal{D}$ has $n$ crossings if $\operatorname{cr}(\mathcal{D})=n$. Unbounded hardness conjecture. For every integer $m$, there exists a diagram of the unknot $\mathcal{D}$ with $n$ crossings such that every sequence of Reidemeister moves from $\mathcal{D}$ to $\hat{\mathcal{D}}$ passes through a diagram with at least $n+m$ crossings. Equivalently, the number of extra crossings required to untangle unknot diagrams is unbounded. The conjecture is folklore; the context notes that the hardest previously known examples had only been verified to require at least three extra crossings.