- What is the cessation of suffering? It is the complete and dispassionate cessation of craving that perpetuates existence, which is attended upon by the passion for enjoyment, and which finds pleasures here and there. This is the cessation of suffering.
Cessation is of two kinds:
- analytical (Skt. pratisaṃkhyā-nirodha; Tib. སོ་སོར་བརྟགས་པའི་འགོག་པ་, sosor takpé gokpa, Wyl. so sor brtags pa'i 'gog pa) and
- non-analytical (Skt. apratisaṃkhyā-nirodha; Tib. བརྟགས་མིན་འགོག་པ་, tak min gokpa, Wyl. brtags min 'gog pa).
This is the unconditioned aspect of the permanent elimination of destructive emotions and other factors to be eliminated, through the force of developing realization of the undefiling path, such as the wisdom of discernment, within the mind.
This does not refer to the ceasing of latent habitual tendencies as a result of analysis and investigation, but rather to the absence of a given thing in a particular place due to an incompleteness of necessary causes and conditions, as in the case of horns on a horse’s head, for instance. Another example which is mentioned in the commentaries is the fact that other types of consciousness do not arise when the eye-consciousness is distracted by a visual form. This also includes all the various forms of non-existence (or absence), such as the absence of a vase in a particular place.
Cessation in Dzogchen
The state of cessation: It is the cessation of all conceptualizations. There are two cessations: the individual analytical cessation is attained through discriminations and analysis by the mind. The non-analytical cessation is attained through contemplating on the ultimate nature with no mental discriminations. 
- Source: The Play in Full, 26.63, translated by the Dharmachakra Translation Committee under the patronage and supervision of 84000: Translating the Words of the Buddha. Read here.
- Tulku Thondup Rinpoche, Buddha Mind: An Anthology of Longchen Rabjam’s Writings on Dzogpa Chenpo, Snow Lion Publications, ISBN 0-937938-66-1, Page 301