6. Let $0<a<1$, if $x_{1}=a, x_{2}=a^{x_{1}}, x_{3}=a^{x_{2}}, \cdots, x_{n}=a^{x_{n-1}}, \cdots$ then the sequence $\left\{x_{n}\right\}$
(A) is increasing
(B) is decreasing
(C) odd terms are increasing, even terms are decreasing
(D) even terms are increasing, odd terms are decreasing
(C)
6. 【Analysis and Solution】First, consider the first three terms of the sequence,
$$
\begin{array}{l}
\because x_{1}=a, x_{2}=a^{a}, x_{3}=a^{a^{a}} \\
\therefore 0<a<1, a<a^{a}<1 . a<a^{a^{a}}<a^{a} .
\end{array}
$$

That is, $x_{1}<x_{2}<x_{3}$.
This already shows that the sequence is neither increasing nor decreasing, and the odd terms are not decreasing either.