I see that you are looking at this:
"§ 44-7-7. Tenancy at will -- Notice required for termination
Sixty days' notice from the landlord or 30 days' notice from the tenant is necessary to terminate a tenancy at will."
It looks to me that (If they are behind in their rent; it is not clear from what you have written that they are) you don't need to terminate the TAW, you need to evict for non-payment.
"§ 44-7-50. Demand for possession; procedure upon a tenant's refusal; concurrent issuance of federal lease termination notice
(a) In all cases where a tenant holds possession of lands or tenements over and beyond the term for which they were rented or leased to the tenant or fails to pay the rent when it becomes due and in all cases where lands or tenements are held and occupied by any tenant at will or sufferance, whether under contract of rent or not, when the owner of the lands or tenements desires possession of the lands or tenements, the owner may, individually or by an agent, attorney in fact, or attorney at law, demand the possession of the property so rented, leased, held, or occupied. If the tenant refuses or fails to deliver possession when so demanded, the owner or the agent, attorney at law, or attorney in fact of the owner may immediately go before the judge of the superior court, the judge of the state court, or the clerk or deputy clerk of either court, or the judge or the clerk or deputy clerk of any other court with jurisdiction over the subject matter, or a magistrate in the district where the land lies and make an affidavit under oath to the facts. The affidavit may likewise be made before a notary public, subject to the same requirements for judicial approval specified in Code Section 18-4-61, relating to garnishment affidavits.
... "
"§ 44-7-51. Issuance of summons; service; time for answer; defenses and counterclaims
(a) When the affidavit provided for in Code Section 44-7-50 is made, the judge of the superior court, the state court, or any other court with jurisdiction over the subject matter or the judge, clerk, or deputy clerk of the magistrate court shall grant and issue a summons to the sheriff or his deputy or to any lawful constable of the county where the land is located. A copy of the summons and a copy of the affidavit shall be personally served upon the defendant. If the sheriff is unable to serve the defendant personally, service may be had by delivering the summons and the affidavit to any person who is sui juris residing on the premises or, if after reasonable effort no such person is found residing on the premises, by posting a copy of the summons and the affidavit on the door of the premises and, on the same day of such posting, by enclosing, directing, stamping, and mailing by first-class mail a copy of the summons and the affidavit to the defendant at his last known address, if any, and making an entry of this action on the affidavit filed in the case.
(b) The summons served on the defendant pursuant to subsection (a) of this Code section shall command and require the tenant to answer either orally or in writing within seven days from the date of the actual service unless the seventh day is a Saturday, a Sunday, or a legal holiday, in which case the answer may be made on the next day which is not a Saturday, a Sunday, or a legal holiday. If the answer is oral, the substance thereof shall be endorsed on the dispossessory affidavit. The answer may contain any legal or equitable defense or counterclaim. The landlord need not appear on the date of the tenant's response. The last possible date to answer shall be stated on the summons.
(c) If service is by posting a copy of the summons and the affidavit on the door of the premises and mailing a copy of the summons and the affidavit to the defendant, as provided in subsection (a) of this Code section, the court shall have jurisdiction to enter a default judgment for possession of the premises in the absence of an answer being filed, but in such instance a default judgment for money owed may not be entered unless the defendant files an answer or otherwise makes an appearance in the case."
"§ 44-7-53. When writ of possession issued; trial of issues; possession pending trial
(a) If the tenant fails to answer as provided in subsection (b) of Code Section 44-7-51, the court shall issue a writ of possession instanter notwithstanding Code Section 9-11-55 or Code Section 9-11-62. The court, without the intervention of a jury, shall not require any further evidence nor hold any hearings and the plaintiff shall be entitled to a verdict and judgment by default for all rents due as if every item and paragraph of the affidavit provided for in Code Section 44-7-50 were supported by proper evidence.
(b) If the tenant answers, a trial of the issues shall be had in accordance with the procedure prescribed for civil actions in courts of record except that if the action is tried in the magistrate court the trial shall be had in accordance with the procedures prescribed for that court. Every effort should be made by the trial court to expedite a trial of the issues. The defendant shall be allowed to remain in possession of the premises pending the final outcome of the litigation; provided, however, that, at the time of his answer, the tenant must pay rent into the registry of the court pursuant to Code Section 44-7-54."
