This simple plugin turn search form of Woocommerce work with ajax.
The search result is display by Ajax.
You can use this shortcode to call search form in widget text
[c4d-woo-ajax-search-form]
or use in php code like this
To use full features, please install and active C4D Plugin Manager and Redux Framework
https://wordpress.org/plugins/c4d-plugin-manager/
https://wordpress.org/plugins/redux-framework/
This plugin is used in C4D Vision - Responsive WooCommerce Theme
You can view here
http://coffee4dev.com/responsive-woocommerce-theme-c4d-vision/