Uninstall another product during installation using WiX

I want to uninstall another application as part of the installation of my MSI file . I currently have the following in WiX:

<Upgrade Id="{586A589B-D6D5-48D3-9B6D-571EF230ED6A}">
    <UpgradeVersion Minimum="$(var.ProductVersion)"
                    Property="NEWERPRODUCTFOUND"
                    OnlyDetect="yes"
                    IncludeMinimum="yes" />
    <UpgradeVersion Minimum="1.0.0"
                    Maximum="$(var.ProductVersion)"
                    Property="PREVIOUSVERSIONSINSTALLED"
                    IncludeMinimum="yes" />
</Upgrade>

<Upgrade Id="{71F6B5D5-8CB9-48C9-B359-4BA22D5ADAF3}">
    <UpgradeVersion Minimum="1.0.0.0"
                    Maximum="3.5.3"
                    Property="OLDAPPFOUND"
                    IncludeMinimum="yes"
                    IncludeMaximum="yes"/>
</Upgrade>

The first section of the update is updating my current MSI file (and it works). The second part is what I'm trying to use to remove another application (which is not the case). Both the current MSI file and the one I’m trying to remove are both set in context for each computer, and I can’t understand why this does not work. How can I fix this problem?