= Solution
For equal <masses> $m$, the <reduced mass> is $m/2$. The <kinetic energy> of their <centre of mass> cannot be removed by an isolated <collision>, since total <momentum> is fixed. Therefore the maximum <energy> available for conversion to internal forms is the initial relative <kinetic energy>,
$$
\boxed{K_{\rm available}=\frac m4|\mathbf v_1-\mathbf v_2|^2.}
$$
It is attained by a <perfectly inelastic collision> in which the final relative <velocity> is zero. This concerns the convertible initial <kinetic energy>, not an arbitrary pre-existing internal <energy> reservoir.
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