@Tobias: The bottom line is that one attains the Arahanthood by clearly seeing the futility of being born ANYWHERE in the 31 realms.
That is reached in steps. First one sees the dangers in cultivating sankhara with the three unwholesome roots. That leads to the Sotapanna stage, and stopping rebirth in the apayas.
Then one sees the futility in born in the kama loka, at a higher level of panna (wisdom). That leads to stopping rebirth in human and deva realms.
All those were done by cultivating sankhara with the three wholesome or good roots. That process continues to the Arahant stage, where one can see the futility in being reborn even in the rupavacara and arupavacara brahma realms.
To look at it from another way: The panna cetasika is optimized only at the Arahant stage. At that point one has attained “Samma Nana”, which is the optimum nana (vision of the true nature of this world is complete), and that leads to “Samma Vimutti” or “total and complete release”.
This is why it is said that: “Attangehi samannagato Sekha, dasa angehi samannagato Arahant” or “one who is completing the Noble Eightfold Path is a Trainee, and one who has completed the next two (Samma Nana and Samma Vimutti) is an Arahant“.
So, when one attains the Arahant stage, there is no NEED to cultivate even the three good roots. “What needs to be done is done; there is nothing nmore to do”.
All six roots lead to rebirth somewhere in the 31 realms. It is just that cultivating the three good roots leads to the “knowledge of the real nature of this world”. But that REQUIRES hearing about Tilakkhana from a Buddha or a true disciple of a Buddha. Otherwise, just cultivating the three good roots will not get one to Nibbana.
You asked: “Can someone post a link to a sutta with explanation of tihetuka, dvihetuka, ahetuka patisandhi? Or can this topic only be found in the Abhidhamma?”
– I think the explanation is available only in Abhidhamma. I could be wrong.