results of the legal autopsy performed on the body were presented; and in establishing the time of death. 213. Given that there is no evidence to show that procedures were carried out to correct these irregularities and, more specifically, the rectification proceeding was not activated in accordance with the legal requirements in force at the time (supra para. 211), which could have provided an effective mechanism for that purpose, the Court finds that in this case it was not possible to correct the initial investigative procedures. For all the foregoing reasons, due diligence and thoroughness of the investigation was impaired. B.1.2. Due diligence in relation to the logical lines of investigation, in gathering and processing of evidence, and reasonable time 214. The Court has established that, in order to ensure effectiveness in the investigation of human rights violations, omissions must be avoided in the gathering of evidence and in following the logical lines of investigation. 324 In this regard, the Court has specified that, when the violent death of a person is involved, the investigation must be conducted in a manner that ensures the proper analysis of the theories regarding the perpetrators. 325 On this point, the Court recalls that it is not for this Court to analyze theories about the perpetrators of the facts arising from the investigation of the facts, and therefore to determine individual responsibilities, a task that is the responsibility of the domestic criminal courts, but rather to assess the actions or omissions of State agents, according to the evidence presented by the parties. 326 Similarly, it is not for the Court to replace the domestic jurisdiction by establishing the specific mode of investigation and prosecution to be followed in a particular case in order to obtain a better or more effective result. Rather, it is for the Court to determine whether or not the steps taken at the domestic level were in violation of the State’s international obligations under Articles 8 and 25 of the American Convention. 327 The Court recalls that a consequence of a lack of diligence in an investigation is that, as time passes, the possibility of collecting and presenting evidence in order to clarify the facts and determine the corresponding responsibilities is unduly limited, with the State thereby contributing to impunity. 328 215. The Court notes that the criminal investigation into A.A.’s death was based on three preliminary theories. First, that his death could have resulted from a dispute with a local group because of his political activities, that is, for political and ideological reasons. Secondly, that his death could have been motivated by conflicts related to the administration of the “Republic of Mexico” Community Self-Management School in the village of Cruce de la Esperanza. Thirdly, that Mr. A.A. was killed because he had witnessed the death of a young man in that area. The first two theories arose in 2004 and the third in 2006. 329 The State mentioned that there was another theory that associated A.A.’s murder with the alleged filing of the complaint in the Case of Gudiel Álvarez et al. ("Diario Militar") before the Inter-American Commission, which Mr. A.A. supposedly signed fifteen days before his death. However, there is no evidence to support this hypothesis. 324 Cf. Case of The Serrano-Cruz Sisters v. El Salvador, supra, paras. 88 and 105, and Case Massacres of El Mozote and nearby places v. El Salvador, supra, para. 257. 325 Cf. Mutatis mutandis, Case of Kawas Fernández v. Honduras, supra, para. 96. 326 Cf. Case of Cantoral Huamaní and García Santa Cruz v. Peru, supra, para. 87, and Case of Gutiérrez and Family v. Argentina, supra, para. 78. 327 Cf. Case of Nogueira de Carvalho et al. v. Brazil, supra, para. 80. 328 Cf. Case of Ibsen Cárdenas and Ibsen Peña v. Bolivia. Merits, Reparations and Costs. Judgment of September 1, 2010 Series C No. 217, para. 172. “The Court has defined impunity as an overall lack of investigation, pursuit, arrest, prosecution and conviction of those responsible” for human rights violations. Cf. Case of the “White Van” (Paniagua Morales et al.) v. Guatemala. Preliminary Objections. Judgment of January 25, 1996. Series C No. 23, para. 173, and Case Manuel Cepeda Vargas v. Colombia, supra, nota 184. 329 Cf. Statement rendered by E.M., a Prosecutor assigned to the case, before the Inter-American Court at the public hearing held on February 5, 2014, and Report prepared by the Agent of the Office of the Human Rights Prosecutor addressed to the Presidential Commission for the Coordination of Human Rights Policies (File of attachments to pleadings and motions brief, pages 7322 to 7327). During the public hearing, a Prosecutor assigned to the investigation described the elements he had to confirm or rule out those hypotheses. On the first hypothesis, he indicated that “no witness appeared to support that hypothesis, other than the statements of Mrs. [B.A.] and of her sister [E.A.].” Regarding the second hypothesis, he stated that “the actual reports by the financial entities and the statements of the teachers confirmed that indeed there had been no misappropriation [of funds] and that Mr. [A.A.]’s administration had expired two years before his death.” Regarding the third hypothesis, he explained that various investigative procedures undertaken “lead us to the hypothesis that the death of Mr. [A.A.] was because he observed and was potentially a witness to a murder.” 64