My male dog peed like a female for the first several months of its life. Then, suddenly, it added a behavior: peeing sideways, with one hind leg raised, on posts and trees. It's a shorter pee, clearly meant to convey territorial signals. It is triggered by artificial posts of all kinds, so the material is not the trigger --suggesting it's either the look of the post or the smell of a previous dog's pee. Why posts and trees? Any other ubiquitous yet discrete location would do --the important thing is a convention where dogs can easily find to smell whether a dog has been there recently or not, and who. 

I suspect the original peeing behavior simply disappears over time because it is triggered by a full bladder, and male adult dogs don't get to fill their bladder before emptying it with the territorial pee.

As for what computation dogs do as they smell the ground routinely during a walk, it's a mystery. Perhaps mate-finding, perhaps prey-tracking, perhaps identification of friends and foes, perhaps all of the above, perhaps something else altogether.

 (Dogs pee on trees while lifting a leg. Art courtesy of Joshua Eisenberg. See also Mathematics,-Language,-Poetry-and-Music:-A-Continuum)