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arXiv · 2411.14559

Union of Finitely Generated Congruences on Ground Term Algebra

Sándor Vágvölgyi
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Abstract

We show that for any ground term equation systems $E$ and $F$, (1) the union of the generated congruences by $E$ and $F$ is a congruence on the ground term algebra if and only if there exists a ground term equation system $H$ such that the congruence generated by $H$ is equal to the union of the congruences generated by $E$ and $F$ if and only if the congruence generated by the union of $E $ and $F$ is equal to the union of the congruences generated by $E $ and $F$, and (2) it is decidable in square time whether the congruence generated by the union of $E$ and $F$ is equal to the union of the congruences generated by $E $ and $F$, where the size of the input is the number of occurrences of symbols in $E$ plus the number of occurrences of symbols in $F$.

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Sándor Vágvölgyi. 2024-11-21. Union of Finitely Generated Congruences on Ground Term Algebra. https://arxiv.org/abs/2411.14559

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