Orlah, Chapter Two, Mishnah 14. This mishnah too deals with two different kinds of prohibitions that combine with one another, and with the dispute between the first Tanna and Rabbi Shimon as to whether such a combination creates a prohibition. What is new in this mishnah: one of the prohibited substances is permitted to a particular group of people - the kohanim.
The case before us:
Leaven of Terumah - permitted to kohanim and forbidden to a non-kohen.
Leaven of kilei hakerem - which grew in a forbidden mixture, and is forbidden to everyone.
These two kinds of leaven fell together into a dough. "Ein b'echad kedei l'chametz" - neither one of them on its own has the power to leaven the dough; but "nitztarfu v'chimtzu" - once they combined, since both are leaven, together they leavened the dough.
The view of the first Tanna - "asur l'zarim u'mutar l'kohanim":
Forbidden to non-kohanim - a non-kohen is forbidden to eat Terumah and is forbidden to eat kilei hakerem, and therefore the two prohibitions combine with one another and create a prohibition.
Permitted to kohanim - Terumah is permitted to a kohen; and as for the kilei hakerem, which is forbidden to him, it does not have enough power on its own to leaven the dough, since it needed the leavening power of the Terumah that is permitted to him. For this reason the dough is permitted to a kohen.
The view of Rabbi Shimon:
Rabbi Shimon disagrees and holds that prohibitions do not combine with one another. Therefore even a non-kohen, who is forbidden to eat both the Terumah and the kilei hakerem, may eat this dough: the leavening came about through the combination of two different kinds of prohibited substances, and in his view two different kinds do not combine to create a prohibition.
In summary: in this mishnah the Tannaim dispute the case of a dough that was leavened by the combination of leaven of Terumah and leaven of kilei hakerem, where neither one alone was enough to leaven it. According to the first Tanna the prohibitions combine, and therefore the dough is forbidden to non-kohanim and permitted to kohanim - for whom the forbidden leaven alone does not leaven the dough; and according to Rabbi Shimon prohibitions do not combine with one another, and therefore the dough is permitted even to non-kohanim.