Sector prices:
AU->SIN in F = 85K
SIN->TPE in J = 30.5K
Total 115K
You're paying 88K.
So you have the advantage of the lower price by paying the through fare. Which is not something a lot of airlines offer if you are including a stopover.
At least in the case of the lower award zones - those most likely not to have F as a connector - the awards are pretty much priced as a
through business class price but charging you differential J->F on sectors where that applies. Example:
AU-SIN-TPE all business class 65K
AU-SIN only J is 62K, F is 85K = difference of 23K
So 65K + 23K = 88K, which is what you paid.
Is the ticket an underlying F ticket? Or is it an underlying J ticket with one sector upgraded to F
Now there are some exceptions to this in that if you are flying to HKG or CGK where they have short-haul F offerings, you'll be getting F/F for a slight saving.