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 $1<a+2<2$, there is $-1<a<0$, at this time, $f(a)<f(a+2)$;
When $a+2 \geqslant 2$, $a \geqslant 0$, at this time,
$$
f(a) \geqslant f(a+2) \text {. }
$$