= Dehn functions under a change of finite presentation
Choose bounded-length substitutions $T$ from the first generating set to the second, and $U$ back. Each substituted <relator> of the second <group presentation> has bounded area in the first, and every generator correction $a(UT(a))^{-1}$ has bounded area. Substitution into a minimal second-presentation diagram and filling the correction strips gives
$$
\delta_1(n)\le C\delta_2(Ln)+Dn.
$$
The reverse construction gives the opposite inequality. Thus the optimal <Dehn functions> are coarsely equivalent, and the existence of a recursive isoperimetric bound, hence solvability of the <word problem for a group>, is independent of the <finite group presentation>.
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