13. Let the function
$$
f(x)=\min \left\{x^{2}-1, x+1,-x+1\right\},
$$

where $\min \{x, y, z\}$ denotes the minimum of $x$, $y$, and $z$. If $f(a+2)>f(a)$, then the range of real number $a$ is $\qquad$.
13. $(-\infty,-2) \cup(-1,0)$.

When $a+2 \leqslant -1$, $a < a+2 \leqslant -1$, at this time, $f(a) < f(a+2)$;
When $-1 < a+2 < 0$, $-3 < a < -2$, at this time, $f(a) \leqslant f(-2) = -1 < f(a+2)$;
When $0 \leqslant a+2 \leqslant 1$, $-2 \leqslant a < -1$, at this time, $f(a) \geqslant f(a+2)$;
When $1 < a+2 < 2$, $-1 < a < 0$, at this time, $f(a) < f(a+2)$;
When $a+2 \geqslant 2$, $a \geqslant 0$, at this time,
$$
f(a) \geqslant f(a+2) .
$$