(Existence of complete Calabi-Yau metric) There is a potential $\phi_{rel}$ such that $\phi=\phi_{glue}+\phi_{rel}$ solves the complex Monge-Ampère equation with decay bound

$$(dd^{c}\phi)^{n}=K_{0}\sqrt{-1}^{n^{2}}\Omega\wedge\overline{\Omega},\quad\left\lVert\phi_{rel}\right\rVert_{k,\alpha,loc}=O(\tilde{\rho}^{-q}),$$

where $q$ can be chosen as any positive number smaller than $\frac{2n-4}{n+2}$.