# Merging incomparable linearizations

**URL:** <https://delvingbitcoin.org/t/merging-incomparable-linearizations/209>\
**Category:** Implementation\
**Tags:** wg-cluster-mempool, mempool\
**Created:** [November 19, 2023, 4:12am UTC](https://delvingbitcoin.org/t/merging-incomparable-linearizations/209 "2023-11-19T04:12:15Z")\
**Posts on this page:** 1\
**Showing post:** 37

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**Author:** ![sipa](https://delvingbitcoin.org/user_avatar/delvingbitcoin.org/sipa/32/1100_2.png) [@sipa](https://delvingbitcoin.org/u/sipa)\
**Post date:** [December 3, 2023, 5:34pm UTC](https://delvingbitcoin.org/t/merging-incomparable-linearizations/209/37 "2023-12-03T17:34:01Z")

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Interesting, it appears that prefix-intersection merging is not associative.

That is, given 3 linearizations A, B, C of a given cluster it is possible that not all three of these are equally good:

- merge(merge(A, B), C)
- merge(merge(A, C), B)
- merge(merge(B, C), A)

This holds even when the inputs, intermediary results, or outputs (or any combination thereof) are [post-processed](https://delvingbitcoin.org/t/linearization-post-processing-o-n-2-fancy-chunking/201).

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