Nearly Euclidean Thurston (NET) maps are described by simple diagrams which admit a natural notion of size. Given a size bound C, there are finitely many diagrams of size at most C. Given a NET map F presented by a diagram of size at most C, the problem of determining whether F is equivalent to a rational function is, in theory, a finite computation. We give bounds for the size of this computation in terms of C and one other natural geometric quantity. This result partially explains the observed effectiveness of the computer program NETmap in deciding rationality.

中文翻译：

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几乎欧几里德·瑟斯顿图的合理性是可以决定的

简单的图表描述了几乎欧几里德的瑟斯顿（NET）地图，这些图表承认了自然的大小概念。给定一个大小范围C，最多有C个大小有限的图。给定一个由大小为C的图表示的NET映射F，理论上确定F是否等于有理函数的问题是有限的计算。我们以C和其他自然几何量为计算上限。该结果部分解释了计算机程序NETmap在确定合理性方面的观察到的有效性。