Tevel and Chulin are intermingled - טבל וחולין מעורבין זה בזה
Summary:
According to רש"י when dividing a partnership each party owns a half of each piece (grain), while according to תוספות it is indeterminable (if we maintain אין ברירה).
She died, yes; she did not die, no - מתה אין לא מתה לא
Summary:
The two ברייתות do not necessarily conflict. The ברייתא of מתה is after the רבנן gave him her פירות. If the woman was not מזכה her פירות, the husband cannot be קורא even after she dies. Even according to ר"ל, if she was מזכה the פירות then he may be מביא וקורא after she dies. It is not like קונה פירות ואח"כ שדה, since he had a vested interest.
Summary:
ביכורים which were fit to be מביא וקורא and then they were not fit to be קורא, they are left to rot; however if they were never fit to be קורא, the rule is מביא ואינו קורא.