Can you give an example of automatic appraisal process? I was reading this slide provided by my prof. of Affective Neuroscience.
I've read that appraisal is considered a constitutive component of emotion by most of the actual theories.
Appraisal is defined as the cognitive act to evaluate the potential impact that an external stimulus may have on me.

Can you provide an example of automatic appraisal?
We make automatic "appraisals" in more or less every waking moment.  We are constantly predicting the potential allostatic consequences of external input and behaving accordingly (e.g., here). Importantly, most appraisals are non-conscious and aren't at all specific to emotions.

Moreover, the automaticity of your appraisals relies on the extent and precision of your prior experience (see here).  If you are used to seeing snakes attack humans, then your appraisal about the danger of snakes will likely be quite fast. 

Thus, there are virtually infinite examples of an automatic appraisal.  Automaticity depends on your prior experience and the precision of incoming sensory input.