Decomposition

Detritus food chain (DFC) begins with detritus or dead organic matter. Detritivores (e.g. earthworm, millipedes, slugs) perform fragmentation process on dead decaying material in any ecosystem. Humus, a dark nutrient rich substance, is degraded by microorganisms releasing inorganic nutrients into the soil. This process is known as mineralisation. By the process of leaching, water soluble inorganic nutrients go down into the soil horizon and get precipitated as unavailable salts.

Detritivores such as earthworms break detritus into smaller particles; this is fragmentation.
In leaching, nutrients go down into the soil; humus is degraded very slowly; catabolism is carried out by bacterial and fungal enzymes.

The important steps of decomposition are fragmentation, leaching, catabolism, humification and mineralisation.
Detritivores such as earthworms break down detritus into smaller particles; this process is called fragmentation.
Catabolism is the degradation of detritus into simpler inorganic substances by bacterial and fungal enzymes.
Humification is the accumulation of dark, amorphous humus, and mineralisation is the release of inorganic nutrients from humus by microbes.
Hence the breakdown of detritus into smaller particles by earthworms is fragmentation.

Decomposition is carried out by the enzymes of bacteria and fungi, and its rate is controlled by the chemical composition of the detritus and by climatic factors, mainly temperature and soil moisture.
Decomposer microbes need water for their growth and for their extracellular enzymes to act. A warm and moist environment favours decomposition, whereas dryness inhibits it.
Fallen logs are made of dry, dead wood with a low moisture content, so microbial activity in them is slow and they decompose slowly. This is the answer given in the answer key.
The surroundings of a fallen log are aerobic, not anaerobic, and wood is rich in cellulose, not low in it.
The chemical nature of wood also contributes: the decomposition rate is slower if the detritus is rich in lignin and chitin, and quicker if it is rich in nitrogen and water-soluble substances like sugars. Wood is rich in lignin and poor in nitrogen, so some books give poor nitrogen content as the answer to this question.

Decomposers break down dead plant and animal remains into simple inorganic substances, which are returned to the soil.
The main decomposers are bacteria (kingdom Monera) and fungi (kingdom Fungi). They secrete enzymes onto the dead matter and absorb the products.
So decomposers belong to Monera and Fungi.