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For a tester in the Test Execution module, they will two local tree views. One view is labled labeled My Executions and the other is All Executions.
My Executions - Assigned executions assigned to the tester or to Anyone will be the only executions that appear in the My Executions view. This view also has the option for the tester to toggle executions assigned to Anyone from appearing.
All Executions - Assigned executions assigned to any tester in the project will appear in the All Executions view.