Bechorot 55: Tithing and the Jordan River

What is the borderline between Beit Jericho and the south?  Our last Mishna stated that the Jordan River is the boundary by which we can judge whether or not animals are tithed.  The Gemara tells us that Rabba bar bar Chana quotes Rabbi Yochanan as teaching that the Jordan River is only a significant divider between Beit Jericho and the south.

The rabbis why only the southern part of the Jorden River (from the area of Jericho to the Dead Sea) is considered to be significant.  Another barita teaches that the Jordan flows from the cavern of Pamyas through the Lake of Sivkhi, the Lake of Tiberias, the Lake of Sodom, and into the Great Sea. The source of the Jordan River is said to be the Banias spring.  It flows to the Chula Lake and to the Kinneret, the Sea of Galilee, and the Dead Sea.  What makes it only significant below Jericho?

Rashi provides an explanation: when the Jordan moves through lakes and marshes in the north, it is not as significant.  Tosafot says that says that the Jordan flows on its own far north of Jericho, related to Binyamin's land, which runs from north of Jericho to the Dead Sea.  Tosafot say this is the "real Jordan".

The Mishna referred to Beit Yericho, which might not have been referring to Jericho but to a settlement called Beit Yerach at the south of the Kinneret.