Calculate the depth of tree in XQuery

depth2.xquery

declare function local:_recurse_depth($element, $count) as xs:integer*
{
    if($element[child::element()])then
        for $child in $element/child::element() return
            local:_recurse_depth($child, $count + 1)
    else
        $count
};

declare function local:depth($x as node()?) as xs:integer
{
   max(local:_recurse_depth($x, ceiling(count($x/child::element()) div (count($x/child::element()) + 0.9))))
};

let $input := <a><b><c><d><e></e></d></c></b><b><a><b /></a></b><b></b></a>
return
  local:depth($input)

Thanks @adamretter.