Answer:
Archaebacteria
Explanation:
Carl Woese categorised the bacteria into two domains called the Archaebacteria and the Eubacteria.
The Archaebacteria is the group of bacteria which can survive in the extreme condition as they posses the characteristics of both the prokaryotes and some eukaryotes. The bacteria are known as the extremophiles.
In the given question, the bacteria which lives in the gut of the human uses methane gas and thus are known as the methanobacteria. These bacteria are considered the archaebacteria as they methane for survival.
Thus, Archaebacteria is correct.
