Step-by-step explanation:
Cellular respiration and photosynthesis are two important physiological processes which formed the basis of life on Earth.
Evolutionary studies have shown that process of photosynthesis evolved earlier in organisms which led to the production of oxygen. This led to the formation of aerobic cellular respiration in organisms.
In the given, a world devoid of the plant is not possible because the plants perform the role of primary producers that is they utilize the available carbon dioxide and water and form the first stable energy molecule called glucose.
This glucose is broken down by the process of cellular respiration to further usable form. These two processes maintain the flow of energy on Earth.
Thus, without these two processes, the fictional world will not be possible.