Guba–Sapir conjecture on superadditivity of Dehn functions

Let $G$ be a finitely presented group. A function is superadditive if $f(m+n)\geq f(m)+f(n)$ for all nonnegative integers $m,n$. Write $f\simeq g$ when the two functions are equivalent up to the standard Dehn-function comparison. Guba–Sapir conjecture. The Dehn function of $G$ is $\simeq$ equivalent to a superadditive function. The analogous question remains open for the abelianised Dehn function; Guba and Sapir noted that failure of the conjecture could indicate a problem with the definition of Dehn function.