I know the Word Problem for finitely presented groups is undecidable in general.
I am looking for software that takes a FPG and a word as input and tries to figure out (using some heuristics) whether it is equal to the neutral element.
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1You could try to run the Knuth-Bendix procedure for a while and reduce with the partial rewriting sytsem obtained. – ahulpke Nov 03 '22 at 06:12