All requests of whatever nature upon the treasury of this state, before any warrant is drawn for the payment of the same, shall be examined, adjusted, and approved by the Department of Administrative Services. All such requests shall be presented to the Director of Administrative Services with such documentation as required in the Nebraska Accounting System Manual on file with the Clerk of the Legislature and shall be audited and settled within two years after the request accrues. No warrants shall be drawn for any request until an appropriation has been made therefor. No warrant for any request for payment or reimbursement of any mileage or other traveling expense shall be issued unless the same is computed strictly in accordance with sections 81-1174 to 81-1177 except as otherwise provided in section 55-157.