I have a site collection. I was told I need a recursive loop to do this.

This is what I've tried:

When the site loads, call getSiteTree() which passes the top level website to my getSubSite() function. From there I check if there are any subsites. I have a boolean but I'm not really using it for anything yet, I've just seen it used before for this type of work. Anyways, from there I check if there are any sub sits, if not I log the end of the branch, if there are, I call the function again using the new url and repeat the process. Looking at my console, it seems to work as intended.

function getSiteTree(){
  var tree = $('#treeviewList');
  var rootsite = window.location.protocol + "//" + window.location.hostname;
  var siteEnd = false;

  getSubSite(rootsite);  
}

function getSubSite(url){
    $().SPServices({
    operation: "GetWebCollection",
    webURL: url,
    async: true,
    completefunc: function(xData, Status) {
        var siteUrl; 
        var siteCount = $(xData.responseXML).find("Web").length;

        if(siteCount == 0){
            console.log("end of branch");
            siteEnd = true;
        }else{
            $(xData.responseXML).find("Web").each(function() {
                siteUrl = $(this).attr("Url");
                console.log(siteUrl);
                getSubSite(siteUrl);
            });
      }
    }
    });
}

My questions: now that I have my sites, I need to take those sites and create something like this but I'm not sure how to accomplish this.

    <li>Site 1
        <ul>
            <li>sub 1.1</li>
            <li>sub 1.2</li>
            <li>sub 1.3</li>
                <ul>
                    <li>1.3.1</li>
                </ul>
            <li>sub 1.4</li>
            <li>sub 1.5</li>
        </ul>
    </li>
    <li>Site 2
        <ul>
            <li>sub 2.1</li>
            <li>sub 2.2</li>
            <li>sub 2.3</li>
                <ul>
                    <li>2.3.1</li>
                    <li>2.3.2</li>
                </ul>
        </ul>
    </li>
</ul>

I have this inital html:

      <div id="treeviewDiv" style="width:200px;height:150px;overflow:scroll">
        <ui id="treeviewList"></ui>
      </div>