{
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  "body": "\n## Definition\n\nLet $S$ be a set, and let $S^{-1} = \\{s^{-1} : s \\in S\\}$ be a set of new symbols, one for each $s \\in S$.\nA word on $S$ is a finite string $t_1 t_2 \\cdots t_n$ with $n \\geq 0$ and each $t_i$ in $S \\cup S^{-1}$.\nA word is reduced when it contains no adjacent pair $s s^{-1}$ or $s^{-1} s$ with $s \\in S$.\n\n## Remarks\n\nThe empty word, with $n = 0$, is reduced.\nRemove adjacent pairs $s s^{-1}$ and $s^{-1} s$, one at a time, until no such pair is left. The result is a reduced word.\nFor example, for $S = \\{a, b, c\\}$, the word $a b^3 c^{-1} c a^{-1} c$ reduces to $a b^3 a^{-1} c$.\nA reduced word is cyclically reduced when its first and last letters are not inverse to each other.\n\n## Explanations\n\n### L1 human\n\nA word is a string of letters and inverse letters.\nIt is reduced when you cannot cancel a letter against its inverse next to it.\nReduced words are the normal forms of the elements of a [[free group|0KTW26C80J]].\n",
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  "name": "Reduced word",
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