that, in principle, if a person was convicted of a criminal offense between June 6, 2006 and December 9, 2011, he or she could have filed a cassation appeal as amended by Law 8503 of 2006 in order to achieve a comprehensive review of the sentence and, failing this, transitory provision III of Law 8837 created the possibility for these persons to appeal possible violations of Article 8(2)(h) of the Convention by filing a motion for review. 265. In view of the foregoing, the Court considers that, in the instant case it is not appropriate to declare a violation of Article 2 of the American Convention because of the way in which the Costa Rican appeals system is regulated, or because of the manner in which the State addressed the situation of persons whose convictions were already final prior to the entry into force of Laws 8503 and 8837. This is because through said reforms, it remedied the deficiencies in the application of the appeal rules that remained after the decisions of the Constitutional Chamber, which since the 1990s indicated that the appeal in cassation should be applied in a way that guarantees the right to a second hearing (supra para. 260). 378 266. Thus, what is required is a case-by-case analysis of the remedies actually filed by the alleged victims in order to determine whether the manner in which they were resolved in the Costa Rican appeals system, taking into account its reforms, respected their right to a comprehensive review of their convictions. 267. In this regard, this Court recalls that an effective remedy means that the analysis of a judicial remedy by the competent authority cannot be reduced to a mere formality, but must examine the reasons invoked by the plaintiff and expressly address these. 379 268. This Court has also pointed out that “the obligation to provide grounds is one of the ‘due guarantees’ included in Article 8(1) to safeguard the right to due process.” 380 The Court has indicated that the grounds “are the exteriorization of the reasoned justification that allows a conclusion to be reached” 381 and implies a rational explanation of the reasons that led the judge to adopt a decision. The importance of this guarantee is linked to the correct administration of justice and the prevention of arbitrary decisions. Likewise, the statement of reasons gives credibility to legal decisions within the framework of a democratic society and demonstrates to the parties that they have been heard. 382 269. This is linked to another aspect that highlights the importance of the reasoning as a guarantee: it provides the possibility, in those cases in which decisions are subject to appeal, to criticize the ruling and obtain a new examination of the issue before a higher court. Thus, the Court has already pointed out that “the grounds for the judicial decision must be provided 378 In this regard, the Court notes that in its judgment in the case of Mendoza et al. v. Argentina, in which it declared a violation of Article 2 of the Convention, positively assessed the “Casal Judgment” of the Supreme Court of Justice in which “the limitation of the appeal in cassation to the so-called issues of law is discarded definitively.” However, it noted that that the criteria evident from the Casal judgment were subsequent to the decisions taken on the appeals in cassation filed on behalf of the presumed victims in this case, which does not occur in this case. Cf. Case of Mendoza et al. v. Argentina, supra, paras. 254 and 255. 379 Cf. Case of López Álvarez v. Honduras. Merits, reparations and costs. Judgment of February 1, 2006. Series C No. 141, para. 96, and Case of Zegarra Marín, para. 179 380 Cf. Case of Apitz Barbera et al. (“First Contentious Administrative Court) v. Venezuela. Preliminary objection, merits, reparations and costs. Judgment of August 5, 2008. Series C No. 182, para. 78, and Case of Zegarra Marín v. Peru, supra, para. 146. 381 Cf. Case of Chaparro Álvarez and Lapo Íñiguez v. Ecuador. Preliminary objections, merits, reparations and costs. Judgment of November 21, 2007. Series C No. 170. para. 107, and Case Flor Freire v. Ecuador, supra, para. 182. 382 Cf. Case of Apitz Barbera et al. (“First Contentious Administrative Court”) v. Venezuela, supra, para. 78, and Case of Zegarra Marín v. Peru, supra, para. 146. 84