of high-redshift ($z\sim $1.5) star-forming galaxies and ULIRGs are also well described by the Kennicutt-Schmidt relation with coefficients $n$=1.17$\pm$0.10 and A=(3.3$\pm$1.5)$\times$10$^{-4}$M$_{\odot}$yr$^{-1}$kpc$^{-2}$, which is comparable to the coefficients we derive from our sample.

In Fig. \[fig:KS\] we plot the star formation and gas-surface surface density for both local and high-redshift star-forming galaxies and ULIRGs from @Genzel10 and overlay the range of acceptable solutions implied by our data. We reiterate that we have adopted $Q$=1 for this analysis and note that if we adopt $Q<$ 1 then the absolute star formation efficiency will be increased proportionally (as shown in Fig. \[fig:KS\]). Nevertheless, this shows that the values of $n$ and $A$ we derive are consistent with the local and high-redshift star-forming galaxies and ULIRGs, but free from uncertainties associated with converting $^{12}$CO luminosities to molecular gas mass, CO excitation or spatial extent of the gas reservoir.

Using the values of $n$ and $A$ we have derived, we infer cold molecular gas masses for the galaxies in our sample of M$_{\rm
  gas}$=10$^{9-10}$M$_{\odot}$ with a median M$_{\rm
  gas}$=7$\pm$2$\times$10$^{9}$M$_{\odot}$. This suggests a cold molecular gas fraction of M$_{\rm gas}$/(M$_{\rm
  gas}$+M$_{\star}$)=0.3$\pm$0.1 but with a range of 10–75%, similar to those derived for other high-redshift starbursts in 