Adding group layer, renaming it from folder name, then adding layers to it from that folder, using ArcPy/Python?

I am trying to use os.walk to go through a directory tree, pull out all the .shp files in it, create a grouplayer in the mxd, rename the grouplayer the folder name, then add the layers from that folder to the group. This is because I have a lot of folders with files in them that represent geologic formations and they don't mean anything once seperated from the name of the formation.

From what I read you can't just add a blank group layer in an mxd from python without first creating a blank one and adding that. The problem starts at the for group_name in rename_group_layer loop. It doesn't even make it through to the print group_name test. Basically it just falls out of the loop from what I can tell.

Then I need to figure out how to add the layers from the folder into the renamed group layer. I have two lines commented out that I think are a start, but I haven't gotten it to go through the renaming loop yet. It will rename the first "New Group Layer" if I put that line above the loop to the correct folder name. I am pretty new to python so any help you can give would be greatly appreciated.

import os
import arcpy


# Set workspace environment to a folder
WS = r'c:\test_define\Appalachian Basin'
arcpy.env.workspace = WS

mxd = arcpy.mapping.MapDocument(r"c:\test_define\test_python_add3.mxd")
df = arcpy.mapping.ListDataFrames(mxd, "layers")[0]

print ("#") *80
for (path, dirs, files) in os.walk(WS):
    for name in files:

        if name.endswith(".shp"):
        print path
           print "^^^^^^^^^^^^^^^^^^ path variable"

            try:
                layers = arcpy.mapping.ListLayers(mxd)
                for layer in layers:
                    if layer.isGroupLayer and layer.name == os.path.basename(path):
                        newLayer = arcpy.mapping.Layer(os.path.join(path, name))
                        arcpy.mapping.AddLayerToGroup(df, layer, newLayer, "BOTTOM")

                    else:
                        groupLayer =                       arcpy.mapping.Layer(r"c:\test_define\empty_group_layer.lyr")  
                        arcpy.mapping.AddLayer(df, groupLayer, "BOTTOM")

                        layers = arcpy.mapping.ListLayers(mxd)
                        for layer in layers:
                            if layer.isGroupLayer and layer.name == "New Group Layer":
                                layer.name = os.path.basename(path)

                        newLayer = arcpy.mapping.Layer(os.path.join(path, name))

                        arcpy.mapping.AddLayerToGroup(df, layer, newLayer, "BOTTOM")

#mxd.save()


# print messages when the tool runs successfully
            print(arcpy.GetMessages(0))
            #print ("+") *50
        except arcpy.ExecuteError:
            print(arcpy.GetMessages(2))


        except Exception as ex:
            print(ex.args[0])

mxd.saveACopy(r"c:\test_define\test.mxd")