The most primitive respiratory process occurring in a living cell is:

Explanation

Glycolysis occurs in the cytoplasm of every living cell, needs no oxygen and no organelle, and is common to bacteria, plants and animals alike, which marks it as the oldest of these pathways, dating from before the atmosphere contained oxygen. The two fermentations are add ons that merely regenerate NAD so glycolysis can continue. The Krebs cycle is later still, since it requires a mitochondrion and oxygen further down the chain.