What is the ruling regarding someone who prayed Dhuhr or Asr and forgot one prostration in each rak'ah, then remembered it upon Tasleem, and how does he rectify his prayer?

If someone prays Dhuhr, or Asr, or Isha and forgets one prostration in each rak'ah, then remembers before the tasleem, there are several opinions on the matter:

Malikis and most Hanbalis: He performs one prostration, making his fourth rak'ah valid, and it is counted as the first. Then he performs three more rak'ahs and prostrates for forgetfulness (sujood al-sahw) before the tasleem. Shafi'is: Only two rak'ahs are valid for him (the first with the second, and the third with the fourth). Hanafis: He performs four prostrations when he remembers, and his prayer is valid.

Ibn Qudamah argued that the first three rak'ahs become invalid by the entry of what follows them before their completion, so only the fourth remains, which he completes with one prostration, then he performs three more rak'ahs. Others, however, held that the entire prayer becomes invalid, considering it a form of trifling.