Fitbit Inc. and Jawbone are fighting hard over patent eligibility. So hard, it might take a bench trial to sort it out.

U.S. District Judge Beth Labson Freeman raised the possibility Thursday after questioning the inventiveness of two Fitbit patents on wearable fitness monitoring devices. The San Jose-based judge broke out her personal running log, complete with sticky notes, while probing whether Fitbit has simply automated the abstract idea of monitoring workouts.