to_parity on Rabin-like automata that are Büchi realizable may still call partial-degeneralization
Here is a case of a Rabin-like input on which to_parity()
calls the partial degeneralization although the input is Büchi-realizable.
HOA: v1
States: 2
Start: 0
AP: 2 "p0" "p1"
Acceptance: 4 (Fin(0)|Fin(1)|Fin(2)) | Inf(3)
properties: trans-labels explicit-labels trans-acc
--BODY--
State: 0
[!0&1] 0 {0 3}
[0&1] 1 {1 2 3}
State: 1
[0&!1] 0 {1 2 3}
[0&!1] 1 {0 2}
--END--
I'd suggest that if an automaton is Rabin-like (or Street-like), then (co-)Büchi realizability should be checked before attempting partial degeneralization. And after partial degeneralization, (co-)Büchi realizability should only be attempted if it wasn't attempted before (if it failed before, I don't see how it would succeed after).