Area of a null-homotopic word ($\mathrm{Area}(w)$)

For a word $w\in F(S)$ representing the identity in $⟨S\mid R⟩$, its area is the least $N$ for whichin $F(S)$, where $r_i\in R$ and ${\epsilon }_i\in \{-1,1\}$.

The Dehn function of a finite presentation isIt measures the worst number of relator applications needed to prove a null word of bounded length.