I'll give this one a go.
1. Determine Routeing Points
Ashchurch (ASC) --->
Barnt Green (BTG),
Cheltenham Spa (CNM) or
Worcester Group
Aberystwyth (AYW) --->
Machynlleth Group
2. Fares Check Rule
Ashchurch - Aberystwyth
Anytime Say Single £39.80 (No Anytime Singles)
Barnt Green - Aberystwyth
Anytime Say Single £35.00 (Permitted)
Cheltenham Spa - Aberystwyth
Anytime Say Single £39.80 (Permitted)
Worcester Stations - Aberystwyth
Anytime Say Single £39.80 (Permitted)
3. Map Check
(1) Barnt Green - Machynlleth Group:
BP+CA
Ashchurch - Barnt Green - Birmingham Group - Smethwick (or Walsall) - Wolverhampton - Shrewsbury - Machynlleth Group - Aberystwyth
(2) Cheltenham Spa - Machynlleth Group:
BD+CE
Ashchurch - Cheltenham Spa - Gloucester - Newport - Hereford - Craven Arms - Shrewsbury - Machynlleth Group - Aberystwyth
(Cannot go the opposite direction after reaching Cheltenham Spa on this map combination as this would involve doubling back between Ashchurch and Cheltenham Spa)
CA+CE
No valid routes via Cheltenham Spa.
(3) Worcester Group - Machynlleth Group:
BD+CE
Ashchurch - Worcester - Hereford - Craven Arms - Shrewsbury - Machynlleth Group - Aberystwyth
CA+CE
Ashchurch - Worcester - Smethwick (- Birmingham Group - Walsall) - Wolverhampton - Shrewsbury - Machynlleth Group - Aberystwyth
All the above routes are valid barring negative easements