<?php
/**
 * Renders a submenu tree.
 *
 * @param string $menu
 *   The internal menu name
 * @param string $path
 *   The path. May be an alias.
 * @return array
 *   Menu tree render array
 */
function EXAMPLE_build_menu_tree($menu, $path) {
  $link = menu_link_get_preferred(drupal_get_normal_path($path));
  if(empty($link['depth'])) {
    return array();
  }
  $parameters = array(
    'min_depth' => $link['depth'] + 1,
    'conditions' => array('p' . $link['depth'] => $link['mlid']),
  );
  $tree = menu_build_tree($menu, $parameters);
  return menu_tree_output($tree);
}