On suggetion:
1. Add a Counter to give each line a unique ID.
2. Run them through a Intersector.
3. On the NODE output of the Intersector - use a listexploder to make one feature per item on the list
4. Merge the Listexploder-features with the real lines (before the Intersector) to get the Geometry of the lines. Everything that comes out of the FeatureMerger_COMPLETE port should now be the lines which intersects. You might want to remove duplicate points etc
Use an AttributeCreator after each input line and overlay line. Create a common attribute name between the two, such as 'intersect'. Give a default value of 1 to the overlays, and default value of 2 to the inputs. Feed both into the Intersector. From the intersected port, run a test filter on the 'intersect' attribute to split them up again.
To find identic common segments of two Line Features, I use the "Chopper" with a Parameter-Value of "2"; this splits Lines into their segments. After that I use the Spatial Relator with a created Attribute("DE9IM=1FFF0FFF2") as Parameter to find exact identical line segments, but one can use "Intersect" as well, to find other types of Intersections, too. See Attached Workbench and Result-Picture. http://www.krimpenfort.org/fme/CommonSegmentFinder_nk_FME2012.fmw