In the case of an appeal from the decision of a mayor sitting as the judge of a mayor's court to the appropriate municipal or county court, if the accused fails to enter into a bond ordered pursuant to section 2933.08 of the Revised Code, the municipal or county court shall commit the accused to jail until he enters into a bond or is discharged by law, and shall render judgment against him for costs and award execution for the costs. He shall not be imprisoned longer than one year.After such a commitment following such an appeal, or after a commitment of not more than one year for not entering into a bond ordered pursuant to section 2933.05 of the Revised Code, if such an appeal was not taken, the court may at any time discharge the accused on his own recognizance.