# GUBS Upper Bound Solver (Extended Abstract)

## TL;DR

The paper introduces GUBS, a constraint solver for inequalities over naturals, which is integrated into HoSA to analyze the complexity of higher-order functional programs, supported by implementation insights and case studies.

## Contribution

It presents GUBS, a novel upper bound solver for natural number inequalities, and demonstrates its application within HoSA for automatic complexity analysis of higher-order programs.

## Key findings

- GUBS effectively solves inequalities involving uninterpreted functions and arithmetic.
- Integration of GUBS into HoSA enables automatic complexity analysis.
- Case studies validate GUBS's practical utility.

## Abstract

In this extended abstract we present the GUBS Upper Bound Solver. GUBS is a dedicated constraint solver over the naturals for inequalities formed over uninterpreted function symbols and standard arithmetic operations. GUBS now forms the backbone of HoSA, a tool for analysing space and time complexity of higher-order functional programs automatically. We give insights about the implemen- tation and report different case studies.