 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 givesThe 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.