Sharepoint Workflow 2013 does not automatically started unless started using user who has site-level contribute permission or has site-owner permission

If I login with an user that has site-level contribute permission or has site-owner permission, then the workflow is triggered normally as expected, but if I login with a user who has contribute permission only on list level, the workflow does not start and following error is thrown:
"HTTP 401 {"error":{"code":"-2147024891, System.UnauthorizedAccessException","Access denied. You do not have permission to perform this action"
How can I trigger the workflow for users who neither have site level contribute permissions and site-owner permission?