A convertible top of this kind is known from practice and comprises a convertible top rod assembly, which, for expanding a convertible top cover, is adjustable between a closed position spanning a vehicle interior and a storage position opening the vehicle interior toward the top.  In the storage position, the convertible top rod assembly is stored in a rear-side convertible top storage box together with the convertible top cover.  Alternatively, instead of a convertible top cover, rigid roof segments can be mounted on the convertible top rod assembly, which form a rigid roof of the respective vehicle in the closed position.  In that case, the roof would be a so-called RHT (retractable hard top).  The convertible top rod assembly comprises a link arrangement on both sides, respectively, in relation to a vertical longitudinal center plane of the convertible top, said link arrangement comprising a main link and a main column, which are pivotably mounted on a vehicle-fixed main bearing, and a front-side first frame element and a second frame element, which is arranged rearward of the first frame element in the closed position and is connected to the first frame element by way of a joint arrangement.  When the convertible top rod assembly is being adjusted, the first frame element can be pivoted relative to the second element by means of an actuating link, which extends along the second frame element.  In the closed position, in which the first frame element and the second frame element are substantially aligned to each other, the first frame element can be secured against pivoting relative to the second frame element by means of a locking element, which is mounted to rotate, interacts with a closing bolt and is adjustable between a locked position and an open position.  In the case of the known convertible top, the closing bolt is arranged on the second frame element.  Due to the arrangement of the closing bolt on the second frame element, it is necessary for the second frame element to extend in the longitudinal direction of the vehicle beyond the joint arrangement connecting the two frame elements in the direction of the first frame element.  This in turn requires that the rear-side convertible top storage box is provided with sufficient dimensions in the longitudinal direction of the vehicle.