Zevachim 12: Half of a Consecrated Animal?

The rabbis continue to sort out the conundrum they have encountered regarding the timing of the paschal offering.  So much has been learned about this particular offering that the rabbis find statements/instructions that contradict each other.  

We are told that an animal that is owned by one person can only be consecrated in whole; if one half of the animal is consecrated, the other half is automatically consecrated as well.  An animal owned by two partners is a different case.  One is only permitted to consecrate his/her part of an animal owned by two partners. 

In such a case, both partners must consecrate the animal in order for it to be fully fit as an offering.  If this doesn't happen, the rabbis agree that an animal disqualified is permanently disqualified, and that an animal half consecrated becomes fully consecrated but not fit for sacrifice if one owner buys the second half of the animal after the first consecration.  Timing is almost everything, it seems.  

The rabbis compare different transgressions and their offerings.  Which pairs have something in common?  At the end of a long discussion, we learn that the dispute that initiated this conversation might have been reviewed as an exercise for students.