We replaced an old fence and can't tell if this wood has been treated or not. Pressure washed a couple of pieces to get the old grime off. https://imgur.com/a/SYsmZ
Other than chemical analysis, or direct knowledge of someone associated with installing the fence or otherwise in the know, there can be no definitive answer to your question as stated in combination with the picture.
However, there are ways to make an educated guess and this picture gives only a small slice of information. Possibly the most useful datum that is needed to adequately answer this question is the age of the fence. That coupled with the species and location would be sufficient to triangulate a reasonably accurate, educated guess.
When in doubt, and the situation indicates the possibility i.e. fencing, assume it is treated. So if you wanted to know whether it would be safe to burn, which is likely all it is good for at this point, and unless you have some of the aforementioned data points, eschew incineration.