Explanation:

- Cauvery: A major river in southern India flowing through Karnataka and Tamil Nadu. Not related to the decommissioned have lock bridge.

- Mahanadi: Originating in central India, it flows through Chhattisgarh and Odisha. No association with this specific bridge.

- Krishna: Third longest river in India, running through Maharashtra, Karnataka, and Andhra Pradesh. The bridge in question isn't built over it.

- Godavari: The second longest river in India, flowing through Maharashtra, Telangana, Andhra Pradesh, Chhattisgarh, and Odisha. The decommissioned have lock bridge is built over this river, making it the correct choice.

Godavari is the correct answer for the river over which decommissioned have lock bridge has been built.