As it has been asked and instead of sharing the slides of my session "Managing permissions when a workflow is executing" from Nintex InspireX 2017, I think that it's more useful to create a blog post 
Minimum permissions to design a workflow (save and publish)
| Site workflows (On Premises) | Site workflows (Office 365) |
|---|---|
| Minimum permissions on the SharePoint site:
| Minimum permissions on the SharePoint site:
|
| List workflows (On Premises) | List workflows (Office 365) |
|---|---|
| Minimum permissions on the SharePoint site containing the list:
Minimum permissions on the SharePoint list:
| Minimum permissions on the SharePoint site containing the list:
Minimum permissions on the SharePoint list:
|
Minimum permissions to start a workflow
| Site workflows (On Premises) | Site workflows (Office 365) |
|---|---|
| Minimum permissions on the SharePoint site:
| Minimum permissions on the SharePoint site:
|
| List workflows (On Premises) | List workflows (Office 365) |
|---|---|
| Minimum permissions on the SharePoint site containing the list:
Minimum permissions on the SharePoint list:
| Minimum permissions on the SharePoint site containing the list:
Minimum permissions on the SharePoint list:
|
Minimum permissions to start a workflow when option "Require manage web rights" is checked (only for On Premises)
| Site workflows | List workflows |
|---|---|
| Minimum permissions on the SharePoint site:
| Minimum permissions on the SharePoint site containing the list:
Minimum permissions on the SharePoint list:
|
You can find more information regarding minimum permissions in Office 365 in this blog post :
