遍历XML文件以递归方式查找产品

I am trying to read remote XML file to find products in a specific category. I am facing issue because XML file has nested categories and each category has products. I need help in preparing a recursive function which will output products from a specific category given the category name. Here is the code i have started with

<?php
    $xml = simplexml_load_file('https://www.deere.com/en/us-en.taxonomy');
    getProducts($xml);

    function getProducts($xml) {
        foreach ($xml as $obj) {
            if ($obj->getName() == 'en_us_tractors') { //if category name is en_us_tractors
                if ($obj->children()) {
                    foreach ($obj->children() as $child) {
                        echo '<h1>' . $child->name . '</h1>';
                        if ($child->products) {
                            foreach ($child->products as $product) {
                                foreach ($product as $p) {
                                    echo 'sku  is ' . $p->sku . '<br>';
                                    echo 'path  is ' . $p->path . '<br>';
                                }
                            }
                        }
                    }                       

                }


            }
        }
    }