Deletion condition for involutory generators

For a group generated by involutions, the deletion condition says that every nonreduced word can be shortened without changing its value by deleting two of its letters.

Arrange the lengths of all consecutive subwords of a word in a triangular grid. Under the folding condition, the boundary between length ascents and descents must contain a folding square. Its equal opposite vertices identify two letters that can be deleted. Induction proves the deletion condition for involutory generators.