When for a period of two years from and after the date of the establishment of a drainage district, or when an appeal is taken or litigation brought against said district within two years from the date such appeal or litigation is finally determined, no contract shall have been let or work done or drainage certificates or bonds issued for the construction of the improvements in such district, a petition may be filed in the office of the auditor, addressed to the board of supervisors, signed by a majority of the persons owning land in such district and who, in the aggregate, own sixty percent or more of all the land embraced in said district, setting forth the above facts and reciting that provision has been made by the petitioners for the payment of all costs and expenses incurred on account of such district. The board shall examine such petition at its next meeting after the filing thereof, and if found to comply with the above requirements, shall dissolve and vacate said district by resolution entered upon its records, to become effective upon the payment of all the costs and expenses incurred in relation to said district. In case of such vacation and dissolution and upon payment of all costs as herein provided, the auditor shall note the same on the drainage record, showing the date when such dissolution became effective.