Singularity categories of skewed-gentle algebras

Let $K$ be an algebraically closed field. Let $(Q,Sp,I)$ be a skewed-gentle triple, $(Q^{sg},I^{sg})$ and $(Q^g,I^g)$ be its corresponding skewed-gentle pair and associated gentle pair respectively. It proves that the skewed-gentle algebra $K{Q}^{sg}\mathrm{/}<I^{sg}>$ is singularity equivalent to $KQ\mathrm{/}<I>$. Moreover, we use $(Q,Sp,I)$ to describe the singularity category of $K{Q}^g\mathrm{/}<I^g>$. As a corollary, we get that $\mathrm{g}\mathrm{l}\mathrm{d}\mathrm{i}\mathrm{m}K{Q}^{sg}\mathrm{/}<I^{sg}><\mathrm{\infty }$ if and only if $\mathrm{g}\mathrm{l}\mathrm{d}\mathrm{i}\mathrm{m}KQ\mathrm{/}<I><\mathrm{\infty }$ if and only if $$\mathrm{g}\mathrm{l}\mathrm{d}\mathrm{i}\mathrm{m}$ KQ^{g}/< I^{g}><\infty$.