In a certain code language, 'BREWING' is written as 'CIFDJMH' and 'ANCIENT' is written as 'BMDRFMU'. How will 'MUSEUMS' be written in that language?

The pattern followed here is split-reversal and increment/decrement.Let's divide each 7-letter word into two halves of 3 letters each, with a middle letter: $[1,2,3][4][5,6,7]$.For BREWING:First 3 letters: $\text{B, R, E}\to$ reverse to $\text{E, R, B}$. Add $+1$ to each:
$$\text{E}+1=\text{F},\text{R}+1=\text{S},\text{B}+1=\text{C}$$
So, the first three letters are rearranged as C, S, F? Let's check the alternative shift or simple positions.Let's look at direct correspondence or reverse pairings:
$$\begin{array}{ccccccc}\text{B}& \text{R}& \text{E}& \text{W}& \text{I}& \text{N}& \text{G}\\ +1\downarrow & -1\downarrow & +1\downarrow & -1\downarrow & +1\downarrow & -1\downarrow & +1\downarrow \\ \text{C}& \text{Q}& \text{F}& \text{V}& \text{J}& \text{M}& \text{H}\end{array}$$
This is close, but the code is CIFDJMH. Let's analyze letter-by-letter:$\text{B}\to \text{C}$ ($+1$)$\text{R}\to \text{I}$ (Opposite letter of R is I)$\text{E}\to \text{F}$ ($+1$)$\text{W}\to \text{D}$ (Opposite letter of W is D)$\text{I}\to \text{J}$ ($+1$)$\text{N}\to \text{M}$ (Opposite letter of N is M)$\text{G}\to \text{H}$ ($+1$)Let's check this logic with ANCIENT:$\text{A}\to +1\to \text{B}$$\text{N}\to \text{Opposite}\to \text{M}$$\text{C}\to +1\to \text{D}$$\text{I}\to \text{Opposite}\to \text{R}$$\text{E}\to +1\to \text{F}$$\text{N}\to \text{Opposite}\to \text{M}$$\text{T}\to +1\to \text{U}$ The code obtained is BMDRFMU, which matches exactly!Now, applying the same pattern to MUSEUMS:$\text{M}\to +1\to \text{N}$$\text{U}\to \text{Opposite}\to \text{F}$$\text{S}\to +1\to \text{T}$$\text{E}\to \text{Opposite}\to \text{V}$$\text{U}\to +1\to \text{V}$$\text{M}\to \text{Opposite}\to \text{N}$$\text{S}\to +1\to \text{T}$ Thus, the code for MUSEUMS is NFTVVNT.