LONG POST ALERT!
The part in parentheses just explains what doubling back means in general in case the reader didn't know....
So you choose to ignore it then?
....That step is not at all concerned with local travel to/from routeing points....
Does that change the definition of a journey?
....I think it is fundamental to how the routeing guide works for long-distance travel: it breaks up the journey into travel to/from appropriate routeing points and travel between those routeing points and considers each part independently, thereby reducing the complexity of the problem. In simplistic terms, you take a local service to a routeing point, a fast service between routeing points, then a local service to your destination. The fares check determines appropriate routeing points....
The Routeing Guide tells us how to find the Permitted Routes for a journey, it does this by breaking the Permitted Routes into smaller sections by way of Routeing Points and maps, there is no evidence that it divides the journey.
If someone took the view that the doubling back test applied to the whole journey, then that would take us back a step and would effectively mean Huddersfield was not an appropriate routeing point, leaving just Stalybridge,...
Step one - Routeing Points for Marsden (and Slaithwaite) are Huddersfield Group and Stalybridge.
Step two - Routeing Point for Manchester Stations is Manchester Group
Step three - No common Routeing Point.
Step four - Stalybridge is an appropriate Routeing Point firstly because it is obvious and secondly because it has a lower fare. Huddersfield could only be considered an appropriate Routeing Point for Marsden (and Slaithwaite) on the basis of the 'rte via Hebden Bridge' fare, for the sake of argument we will say it is an appropriate Routeing Point.
Step five - Both appropriate Routeing Points for Marsden (and Slaithwaite) have direct services over the shortest route.
Step six - Stalybridge-Manchester gives maps GM and MR (NOTE: Hebden Bridge does not appear on either of these maps). Huddersfield-Manchester gives us map GM.
(NOTE: Tickets routed via Hebden Bridge are not appropriate to travel via Stalybridge (but may be used that way if the fare is higher than an appropriate fare) and so routes via Hebden Bridge have been ignored for this example, though any higher fare would also be valid on routes via Hebden Bridge.)
Step seven - These maps give us routes of:
Huddersfield Group-Stalybridge-Ashton/Guide Bridge-Manchester Group (GM)
Stalybridge-Ashton/Guide Bridge-Manchester Group (GM)
Stalybridge-Guide Bridge-Manchester Group (MR)
The first would require the ticket holder to double back in a single journey and is therefore not permitted, the other two would not.
At what point have I gone back a step?
....and there'd be little practical difference between DIRECT and ANY PERMITTED, and I'd want to ask why VIA HUDDERSFIELD wasn't introduced instead and how many more easements are missing in similar situations across the network.
'Rte Any Permitted' costs more than the 'rte via Hebden Bridge' fare and is therefore valid via Hebden Bridge. 'Rte Direct' costs less than 'Rte via Hebden Bridge' fare and would therefore not be valid via Hebden Bridge.
And with my bolding:
FINDING APPROPRIATE ROUTEING POINTS
Any routeing point can be used, provided
it does not
- use routes not permitted for the journey
So to
find the appropriate routeing points, which is necessary before we can work out the permitted routes, we must first know the routes that are not permitted? Chicken and egg?....
You have taken them as an option, one or another, they are not, they must all be adhered to.
FINDING APPROPRIATE ROUTEING POINTS
Any routeing point can be used, provided it does not
- use routes not permitted for the journey
- cause doubling back (passing through the same station twice between origin and destination)
- make the journey double back through the origin or destination station unless the fare permits (for example Ealing Broadway to Swindon via London).
- allow travel by a route which does not satisfy the fare-check rule. This rule is explained in the box below.