Log-behavior of the root sequences of P-recursive sequences

In recent years, Sun has proposed numerous conjectures regarding the log-concavity of root sequences \{\sqrt[n]{a_n}}_{n\geqslant 1}. We establish criteria for the asymptotic log-concavity of \{\sqrt[n]{a_n}}_{n\geqslant 1} and the asymptotic ratio log-convexity of \{\sqrt[n]{a_n}}_{n\geqslant 1} for $P$-recursive sequences \{\sqrt[n]{a_n}}_{n\geqslant{0}}. Additionally, by the aid of symbolic computation, we present a systematic approach to determine the explicit integer $N$ such that the sequence \{\sqrt[n]{a_n}}_{n\geqslant{N}} is log-concave and the sequence \{\sqrt[n]{a_n}}_{n\geqslant N} is ratio log-convex.