Business Automation & Magento Integration

[Uldis]

I was wondering if there is an existing solution for an integration between Business Automation 6.x and Magento (Community Edition 1.9.2.2 and 2.0.0, latest - http://magento.com).

The idea is to have a Magento storefront with keeping Business Automation in charge of...
- Customer accounts
- Shopping cart
- Checkout
- Add to cart (requests goes to Business Automation)

If there's no such solution, could you please point me to the relevant documentation for creating such an integration.

Many thanks.