Could the Snapper transformer help in this case (set snapping tolerance to snap the short endpoints to the intersecting line)?

Hi @is, unlike ArcGIS, FME computes geometries with full precision of double precision floating point number. I therefore think it could also be possible that the intersection shown on the display was just a computational error of ArcGIS and the lines aren't intersecting in the full precision actually.

Have you confirmed that there is an actual intersection by seeing the full precision coordinate values of relevant vertices? You can see every coordinate values with the Feature Information window of FME Data Inspector.

Yes, intersections are real - ArcGIS Check Geometry tool shows this parts as error geometries.

I don't think the ArcGIS Check Geometry tool could detect intersections between different lines. If you need to split a line at its self-intersections, set Yes to the "Split Self-Intersecting Features" parameter in the Intersector transformer.

Thanks for opinion, but the problem is that "Yes" to the "Split Self-Intersecting Features" parameter in the Intersector transformer is already set, but supersmall loops stays unsplitted as they are.

Looks like Snapper (vertex snapping mode) could help, like @erik_jan suggests.

It sounds like the intersections are not true intersections but are lines which are within a certain distance of each other which is smaller than a specified tolerance? FME will not report these in a straightforward way as the lines do not truly intersect