What is the case for the dinosaur classification system where the two orders are phytodinosauria and the theropoda(what are the synonymorphies(did i spell that right)?)?

I don't think there is any serious case for the phytodinosauria (Bob Bakker's hypothesis that the sauropod and prosauropod dinsoaurs are more closely related to the ornithischains that the theropods).

I honestly can't think of a proper scientific study in which this result was recovered, and the traditional split between the ornithischians and the saurischians is well supported by a number of anatomical features. Most notably, saurischians have pneumatic bones (they are full of holes that would be taken up with air sacs extending from the lungs as in birds) and the ornithischians do not.