What are Lucene indexes and how does a reindex action work?

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Terminology reindexing is performed per client, for all language combinations at once, not separately.

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How to recognize translation memory/terminology indexing issues

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How to recognize translation memory (TM) indexing issues

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Actually, there is only one XTM Cloud UI "symptom" that would indicate a need to reindex the terminology. If a particular term is visible in the terminology database in the UI for a particular language combination, make sure that you have included it in your current project (by creating the project for the customer that holds this terminology data or by incorporating the relevant resources from another customer in the project). If you now enter XTM Workbench in "Edit" mode, activate a segment and see that the term in question will not highlight blue, this might be a valid reason to perform reindexing.

Also check if the Disable term decoration option is activated globally in Configuration → Settings → Translation → Terminology → Terminology options:

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You have it switched off during project creation:

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