We present a technique to infer lower bounds on the worst-case runtime complexity of integer programs, where in contrast to earlier work, our approach is not restricted to tail-recursion. Our technique constructs symbolic representations of program executions using a framework for iterative, under-approximating program simplification. The core of this simplification is a method for (under-approximating) program acceleration based on recurrence solving and a variation of ranking functions. Afterwards, we deduce asymptotic lower bounds from the resulting simplified programs using a special-purpose calculus and an SMT encoding. We implemented our technique in our tool LoAT and show that it infers non-trivial lower bounds for a large class of examples.

中文翻译：

---

推断整数程序的较低运行时界限

我们提出了一种推断技术降低整数程序的最坏情况运行时复杂度的界限，与早期的工作相比，我们的方法不限于尾递归。我们的技术使用一个用于迭代、欠近似程序简化的框架来构建程序执行的符号表示。这种简化的核心是一种基于递归求解和排序函数变体的（欠近似）程序加速方法。之后，我们推断渐近的使用专用微积分和 SMT 编码得到的简化程序的下限。我们在我们的工具 LoAT 中实现了我们的技术，并表明它为大量示例推断出非平凡的下限。