I guess you mean that the worklfow has been started with this user? So the initiator has been set as appropriated property. Now you have to iterate over all workflowdefinitions, and all workflows iteself to find out, whether the initiator matches with the selected one. Now you can delete this workflow.
I would suggest to select the database itself to retrieve the active workflows and get active workflows from this point of view in place of using Alfrescos API as its getting realy slow.