We explore the Weihrauch degree of the problems ``find a bad sequence in a non-well quasi order'' ($\mathsf{BS}$) and ``find a descending sequence in an ill-founded linear order'' ($\mathsf{DS}$). We prove that $\mathsf{DS}$ is strictly Weihrauch reducible to $\mathsf{BS}$, correcting our mistaken claim in [arXiv:2010.03840]. This is done by separating their respective first-order parts. On the other hand, we show that $\mathsf{BS}$ and $\mathsf{DS}$ have the same finitary and deterministic parts, confirming that $\mathsf{BS}$ and $\mathsf{DS}$ have very similar uniform computational strength. We prove that K\"onig's lemma $\mathsf{KL}$ and the problem $\mathsf{wList}_{2^{\mathbb{N}},\leq\omega}$ of enumerating a given non-empty countable closed subset of $2^{\mathbb{N}}$ are not Weihrauch reducible to $\mathsf{DS}$ or $\mathsf{BS}$, resolving two main open questions raised in [arXiv:2010.03840]. We also answer the question, raised in [arXiv:1804.10968], on the existence of a ``parallel quotient'' operator, and study the behavior of $\mathsf{BS}$ and $\mathsf{DS}$ under the quotient with some known problems.

翻译：我们探讨了问题“在非良拟序中寻找坏序列”（$\mathsf{BS}$）与“在非良基线性序中寻找降序列”（$\mathsf{DS}$）的Weihrauch度。我们证明了$\mathsf{DS}$严格Weihrauch可归约于$\mathsf{BS}$，从而修正了我们在[arXiv:2010.03840]中的错误论断。这是通过分离它们各自的一阶部分实现的。另一方面，我们证明了$\mathsf{BS}$与$\mathsf{DS}$具有相同的有限部分和确定性部分，这确认了$\mathsf{BS}$与$\mathsf{DS}$具有非常相近的一致计算强度。我们证明了K\"onig引理$\mathsf{KL}$以及枚举给定$2^{\mathbb{N}}$的非空可数闭子集的问题$\mathsf{wList}_{2^{\mathbb{N}},\leq\omega}$均不能Weihrauch归约到$\mathsf{DS}$或$\mathsf{BS}$，从而解决了[arXiv:2010.03840]中提出的两个主要开放问题。我们还回答了[arXiv:1804.10968]中提出的关于“平行商”算子存在性的问题，并研究了$\mathsf{BS}$和$\mathsf{DS}$在与某些已知问题取商下的行为。