SN 2.12.23
The Buddha teaches a variation of the paṭicca samuppāda which works back from the elimination of the corrupting influences (āsavas) and he states that there is no destroying the corrupting influences without knowing and seeing this progression.
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Index of Available translations: [SN 2.12.023]
A very important sutta! Sometimes called the positive version of the paṭicca samuppāda.
This is the issue with regard to this sutta: If you follow the sequence through without careful reflection on the idea that there is no thing that is the self, you can come to the conclusion that once a living being has become, it will end in Nibbāna. No need to do anything. This statement has been made, and is one of the fundamental bases of Mahayana Buddhism.
The formulation in this sutta lead to the statement that all things (dhammas) end in Nibbāna and from there to the belief that this means 'all beings', and that this could and would be attained by all beings simultaneously (and further, that we should put off attaining Nibbāna until that happens).
But the Buddha is not saying this. He is saying that it is seeing the process which leads to the conclusion in Nibbāna. There is no statement there that the whole process occurs for each occurrence of blindness bringing consciousness into existence.
There is nothing in this formula which stipulates the Time the process will consume.
There is no statement in the suttas and there is no basis in the theory of the arising of living beings that is the paṭicca samuppāda, for a belief that there is a fixed number of beings, or that new beings are not arising all the time.
In fact the opposite is clearly indicated.
There is no thing there that is 'the living being.' Like bubbles in beer, living beings arise as a result of conditions; it is a construction made up of name/form and consciousness brought into self-aware existence from factors, primarily blindness, the idea 'I am', and the desire to be, and the supply of these factors, and primarily of blindness in the limitless universe is limitless.
The statement is also made in the form: "All Dhammas (teachings of the Buddhas) end in Nibbāna." This statement, while true in spirit, is not absolutely true. The Buddha taught many things at many different levels, not all of which pointed directly to and end in Nibbāna. For example he taught generosity, loving kindness, care for parents, and self-control as a matter of making good kamma.
Of Related Interest:
[SN 2.12.23] 
Transcendental Dependent Arising Translation & Exposition of the Upanisa Sutta, Bhk. Bodhi.
AN10.2
AN11.2
AN10.61
AN10.62
