In this talk, we analyze the Borel complexity of topological conjugacy of pointed Cantor minimal systems. We prove that the topological conjugacy relation on pointed Cantor minimal systems is Borel bireducible with the Borel equivalence relation $E_{cntble}$ on $\mathbb{R}^{\mathbb{N}}$ defined by $x E_{cntble} y \Leftrightarrow \{x_i:i \in \mathbb{N}\}=\{y_i:i \in \mathbb{N}\}$. We also show that $E_{cntble}$ is a lower bound for the Borel complexity of topological conjugacy of Cantor minimal systems. As an application of the former result, we will show that there exists no equivalence-invariant Borel way of attaching orders to simple Bratteli diagrams and obtaining properly ordered Bratteli diagrams.