(Path Distance—Help | ArcGIS for Desktop)The Path Distance tools are comparable to the Cost Distance tools in that both determine the minimum accumulative travel cost from a source to each location on a raster surface. However, the Path Distance tools add more complexity to the analysis by being able to accommodate for the actual surface distance as well as other horizontal and vertical factors.
To me, the preposition "for" is redundant! What is your opinion? Does it work for you?