Complex sentence: The patriarchal succession was not disputed until the Council of Chalcedon in 451, after which point there were rival Melkite and non-Chalcedonian claimants to the see, now known as the Greek Orthodox Patriarch of Antioch and the Syriac Orthodox Patriarch of Antioch, respectively.
Split into simpler sentences: The patriarchal succession was not disputed until the Council of Chalcedon in 451, after which point there were rival Melkite and non-Chalcedonian claimants to the see. Their Orthodox counterparts are the Greek Orthodox Patriarch of Antioch and the Syriac Orthodox Patriarch of Antioch, respectively.