Tosefta for Chullin 59:20

[If] someone's chicken was stolen, and he came and found it slaughtered, [or] if his livestock was stolen, and he came and found it slaughtered, Rabbi Chananiah, son of Rabbi Yosei HaGalili invalidates it and Rabbi Yehuda validates it. Said Rebbi, the words of Chananiah son of Rabbi Yosei HaGalili are preferable as to one who finds it inside a house, and the words of Rabbi Yehuda [are preferable] as to one who finds it in a trash heap. As to one who finds a chicken slaughtered in the market, and similarly who gave a chicken to someone from the market to slaughter, and does not know what his practice is, we follow after the majority. If a knife fell and he slaughtered, or if he pressed down and slaughtered it (Hul. 30a:15), or if he slaughtered it from above, it is [considered] carrion and it imparts impurity by carrying. [If] he was slaughtering and he trembled, or became exhausted, or his friend pushed him, or the wind pushed him, or the knife fell from his hand and he picked it back up, or the corner of his cloak fell and he picked it back up, or he waited the amount of time [it would take to perform] another slaughter, [the slaughter] is invalid (Hul. 2:3). Rabbi Shimon says, [if the delay was] as long as [it would take to slaughter] another livestock. [If] he slaughtered the gullet and waited as long as [it would take to perform] a slaughter, and afterwards he severed the gullet [not in a standard manner (see Hul. 32a:17)], or he sharpened the knife under the gullet, and it was severed, or he sharpened the knife under the windpipe and it was severed, or he sharpened the knife under both of them, and both of them were severed, Rabbi Yeshevav says, it is [considered] carrion (Hul. 2:4) and it imparts impurity by carrying. Rabbi Akiva says, it is [considered merely] a tereifah, and its slaughter is ritually pure. Rabbi Yeshevav said to him, "If you remember, that Rabbi Yehoshua would teach (i.e., repeat the oral tradition) that anything that becomes unfit during the act of slaughter is [considered] carrion, and imparts impurity by carrying, [but anything that is rendered unfit] before the act of slaughter is a tereifah, and the slaughter renders it ritually pure." Rabbi Akiva [then] retracted [his ruling] and began teaching in accordance with the statement of Rabbi Yeshevav. [If] he slaughtered a small part of the gullet and waited as long as [it would take to perform another] slaughter, and afterwards he [completed] slaughtering both [simanim], or if the gullet was punctured and afterwards he slaughtered both [simanim], [the slaughter is considered] a tereifah and the slaughter renders it ritually pure.