Answer: Please pay attention to the following narration:

مُحَمَّدُ بْنُ عَلِيِّ بْنِ الْحُسَيْنِ بِإِسْنَادِهِ عَنْ مُعَاوِيَةَ بْنِ وَهْبٍ عَنْ أَبِي عَبْدِ اللَّهِ أَنَّهُ قَالَ: إِذَا دَخَلْتَ بَلَداً وَ أَنْتَ تُرِيدُ الْمُقَامَ عَشَرَةَ أَيَّامٍ فَأَتِمَّ الصَّلَاةَ حِينَ تَقْدَمُ وَ إِنْ أَرَدْتَ الْمُقَامَ دُونَ الْعَشَرَةِ فَقَصِّرْ وَ إِنْ أَقَمْتَ تَقُولُ غَداً أَخْرُجُ أَوْ بَعْدَ غَدٍ وَ لَمْ تُجْمِعْ عَلَى عَشَرَةٍ فَقَصِّرْ مَا بَيْنَكَ وَ بَيْنَ شَهْرٍ فَإِذَا تَمَّ الشَّهْرُ فَأَتِمَّ الصَّلَاةَ قَالَ قُلْتُ: إِنْ دَخَلْتُ بَلَداً أَوَّلَ يَوْمٍ مِنْ شَهْرِ رَمَضَانَ- وَ لَسْتُ أُرِيدُ أَنْ أُقِيمَ عَشْراً قَالَ قَصِّرْ وَ أَفْطِرْ قُلْتُ فَإِنْ مَكَثْتُ كَذَلِكَ أَقُولُ: غَداً أَوْ بَعْدَ غَدٍ فَأُفْطِرُ الشَّهْرَ كُلَّهُ وَ أُقَصِّرُ قَالَ نَعَمْ هَذَا وَاحِدٌ إِذَا قَصَّرْتَ أَفْطَرْتَ وَ إِذَا أَفْطَرْتَ قَصَّرْتَ

📚Man La Yahduruhu al-Faqih, Vol. 1, p. 437

Translation: Imam Sadiq (peace be upon him) said: When you enter a city and you intend to stay there for (at least) ten days, from the moment you enter that city, pray the full prayer. And if you intend to stay there for less than ten days, pray the shortened prayer. But if you stay in that city and you say 'I will leave tomorrow' or 'the day after tomorrow' (and it is not clear how long you will stay there) and you do not have a firm intention to stay for ten days, pray the shortened prayer for one month. And when one month is complete, from then on, pray the full prayer. The narrator said: I said: What if I enter that city on the first day of the month of Ramadan and I do not intend to stay for ten days? He said: Pray the shortened prayer and break the fast. I said: If I continue to stay like this and say 'I will leave tomorrow or the day after' (and the duration of my stay was not clear), should I break the fast for the entire month of Ramadan and pray the shortened prayer? He said: Yes, these two cases are one: when you pray the shortened prayer, you also break the fast, and when you break the fast, you also pray the shortened prayer.

✅Based on the above narration, a person who enters a city and it is not clear how long he will stay there and he does not have a firm intention to stay for ten days, his prayer is shortened and his fast is broken for up to one month. And if he stays for more than one month, his prayer and fasting become complete. For example, a person who goes to a city to collect a debt or perform a task, but it is not clear whether this will take one day, two days, or more. Such a person's prayer and fasting are shortened for up to one month, and if he stays in that place after thirty days, his prayer and fasting are complete.

✅Also, pay attention to the following hadith:

عَنْ أَبِي أَيُّوبَ قَالَ: سَأَلَ مُحَمَّدُ بْنُ مُسْلِمٍ أَبَا عَبْدِ اللَّهِ وَ أَنَا أَسْمَعُ عَنِ الْمُسَافِرِ إِنْ حَدَّثَ نَفْسَهُ بِإِقَامَةِ عَشَرَةِ أَيَّامٍ قَالَ فَلْيُتِمَّ الصَّلَاةَ فَإِنْ لَمْ يَدْرِ مَا يُقِيمُ يَوْماً أَوْ أَكْثَرَ فَلْيَعُدَّ ثَلَاثِينَ يَوْماً ثُمَّ لْيُتِمَّ وَ إِنْ كَانَ أَقَامَ يَوْماً أَوْ صَلَاةً وَاحِدَةً

Translation: Abu Ayyub said: Muhammad ibn Muslim, while I was also listening, asked Imam Sadiq (peace be upon him): What if the traveler intends and plans to stay for ten days? He said: He should pray the full prayer. And if he does not know how long he will stay, one day or more, he should count thirty days and then pray the full prayer.

✅The lunar month is sometimes thirty days and sometimes twenty-nine days. And according to the above hadith, what is mentioned in the first narration, that after one month his prayer is complete, the standard is thirty days, and after exactly thirty days have passed, if he remains in that city, his prayer and fasting are complete, even if it is only for one more prayer in that city.

Traveler's prayer

Traveler's fast

Completing the shortened prayer