Parse a HTML menu to an Array or a JSON

Question

I have the following menu:

<ul id="myMenu" >
    <li><a href="#" >Home</a></li>

    <li><a href="#">Services</a>
        <ul>
            <li><a href="#">Residential</a>
                <ul>
                    <li><a href="">Sub Page 1</a></li>
                    <li><a href="">Sub Page 2</a></li>
                </ul>
            </li>
            <li><a href="#">Commercial</a></li>
        </ul>
    </li>

    <li><a href="#">Prices</a></li>

    <li><a href="#">Contact Us</a></li>
</ul>

I want to convert this HTML menu to an array or a JSON (I'd prefer JSON format) to be something like this:

"menu" : [
  {
    "title" : "Home",
    "href" : "blabla.com"
  }
  ,
  {
    "title" : "Service",
    "href" : "blabla.com",
    "pages" : 
      [
        {
          "title" : "Residential",
          "href" : "blabla.com",
          "pages" : [
            {
              "title" : "Sub Page1",
              "href" : "blabla.com",
            },
            
            {
              "title" : "Sub Page2",
              "href" : "blabla.com",
            }
            ]
        }
      ]
  },
  {
    "title" : "Prices",
    "href" : "blabla.com"
  },
  
    {
    "title" : "Contact Us",
    "href" : "blabla.com"
  }


  
]

I use the following function to convert HTML to an array (I know this is complicated to do, so, You don't need to implement it, It's ready to use):

function xmlstr_to_array($xmlstr)
{
    $doc = new DOMDocument();
    $doc->loadHTML($xmlstr);

     return domnode_to_array($doc->documentElement);
}
function domnode_to_array($node) {
    $output = array();

    switch ($node->nodeType)
    {
        case XML_CDATA_SECTION_NODE:

        case XML_ATTRIBUTE_NODE:

        //If it's only Text
        case XML_TEXT_NODE:
            $output = trim($node->textContent);
            break;

        //If it's an xml node, then search for children
        case XML_ELEMENT_NODE:

            for ($i = 0, $m = $node->childNodes->length; $i < $m; $i++)
            {

                $child  = $node->childNodes->item($i);
                $v      = domnode_to_array($child);

                if(isset($child->tagName))
                {
                    $t = $child->tagName;

                    if(!isset($output[$t]))
                    {
                        $output[$t] = array();
                    }

                    //Eliminate li please
                    if ($t == 'li')
                    {
                        $output[$t][] = $v;
                    }

                    else
                    {
                        $output[$t][] = $v;
                    }
                }
                else if($v)
                {
                    $output['title']         = (string) $v;
                    $output['href']         = 'blablabla.com';
                }
            }

            if(is_array($output))
            {
                if($node->attributes->length) {
                    $a = array();
                    foreach($node->attributes as $attrName => $attrNode) {
                        $a[$attrName] = (string) $attrNode->value;
                    }
//                    $output['@attributes'] = $a;
                }
                foreach ($output as $t => $v) {
                    if(is_array($v) && count($v)==1 && $t!='@attributes') {
//                        $output[$t] = $v[0];
                        $output[$t] = $v[0];
                    }
                }
            }

            break;
    }

    return $output;
}

I tried to use something like this to parse the whole array (and convert it later to JSON) but I faild:

function parse($data)
{
$arr = [];

//Rules
// ul = there's a sub-page
$i = 0;
foreach ($data as $conv)
{
    foreach ($conv as $k => $v)
    {
        //if <a> then it means it's an item. since all items starts with <a>
        if (isset($v['a']))
        {
           $arr[$i] = $v['a'];

            if (isset($v['a']['ul']))
            {

            }