Identify private pipes which are in between public pipes (water network)

Nado

Hello, l try to identify private pipes in between public pipes. Here it will be the green line (private) between 2 purple lines (public).

I tried to create a topology, here are the options l got :

Could anyone help me to define how l should do ? Is the topology the right tool to get my result ? Any other ways ? Thanks :)

mfarooqui

Are the public and private pipes stored in separate feature classes/layers, or are they in the same line feature class and distinguished by an attribute? Also, are the endpoints of the private pipes snapped to the public pipe features? This will help determine whether a topology rule or an endpoint/spatial-selection approach is more appropriate.