Try the Intersector, or the TopologyBuilder transformers. Both will split lines like "Planarize" as far as I can tell

Thank you tomf

But how to clean duplicates (overlaps) being identified by Intersector and TopologyBuilder tools?

WIth the Intersector the overlapping line segments are reduced to a single line segment. From the Edge port of the TopologyBuilder, you can use a Matcher to find matching geometries and just keep the SingleMatched and NotMatched features. For a pure geometry match unselect Check Attributes in the Matcher parameters. You can also use a tolerance here to find close geometry matches

It appears that the TopologyBuilder splits the lines where they are overlapped while the Matcher has no thing to do when it comes to clean the duplication.

The Matcher works fine when you set the parameters as I suggested. The only thing else I added (which made no difference in this example) was to allow Lenient Geometry matching, i.e. drawing direction is ignored when matching geometry.

I get 4 Matched features, 2 SingleMatched and 4 NotMatched. By taking just SingleMatched and NotMatched ports, the overlapping line parts are dropped.

Note: the Intersector outputs just 6 line segments and 8 nodes. So, here the overlapping line segments are already cleaned.

Thank you tomf.

The intersector, topolgybuilder, and macher tools appear to do the job