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james-d-mitchell merged 2 commits into from
Aug 28, 2026
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Update rpo and rev_rpo #485

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baa1b6a
Update rpo and rev_rpo
Joseph-Edwards Aug 28, 2026
fe32261
KnuthBendix: register missing types
Joseph-Edwards Aug 28, 2026
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21 changes: 21 additions & 0 deletions docs/source/data-structures/order/index.rst
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Expand Up @@ -14,6 +14,27 @@ This page contains the documentation for classes and several functions for
comparing words (i.e. lists of integers ``list[int]`` or strings ``str``) with
respect to certain reduction orderings.

Some of the orders are generalisations of others. In particular,
when the weight of every generator is the same:

- :any:`len_wt_lex_cmp` is a generalisation of :any:`lenlex_cmp`;
- :any:`rev_len_wt_lex_cmp` is a generalisation of :any:`rev_lenlex_cmp`;
- :any:`wt_lenlex_cmp` is a generalisation of :any:`lenlex_cmp`; and
- :any:`rev_wt_lenlex_cmp` is a generalisation of :any:`rev_lenlex_cmp`;
- :any:`wt_lex_cmp` is a generalisation of :any:`lex_cmp`; and
- :any:`rev_wt_lex_cmp` is a generalisation of :any:`rev_lex_cmp`.

Additionally:

- :any:`wr_cmp` is a generalisation of :any:`lenlex_cmp` when all
of the generators have the same level;
- :any:`rev_wr_cmp` is a generalisation of :any:`rev_lenlex_cmp` when all
of the generators have the same level;
- :any:`wr_cmp` is a generalisation of :any:`rev_rpo_cmp` when all
of the generators have a different level; and
- :any:`rev_wr_cmp` is a generalisation of :any:`rpo_cmp` when all
of the generators have a different level.

.. seealso::

- :any:`Order`
Expand Down
13 changes: 13 additions & 0 deletions docs/source/libsemigroups.bib
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Expand Up @@ -672,3 +672,16 @@ @article{Du2026aa
volume = {150},
year = {2026}
}

@article{Dershowitz1982aa,
title = {Orderings for term-rewriting systems},
journal = {Theoretical Computer Science},
volume = {17},
number = {3},
pages = {279-301},
year = {1982},
issn = {0304-3975},
doi = {https://doi.org/10.1016/0304-3975(82)90026-3},
url = {https://www.sciencedirect.com/science/article/pii/0304397582900263},
author = {Nachum Dershowitz},
}
14 changes: 14 additions & 0 deletions docs/source/main-algorithms/knuth-bendix/to-knuth-bendix.rst
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Expand Up @@ -110,6 +110,8 @@ and the third item one of:
with short-lex reduction ordering.
- :any:`Order.rpo` for constructing a :any:`KnuthBendix`
with recursive-path reduction ordering.
- :any:`Order.rev_rpo` for constructing a :any:`KnuthBendix`
with reverse recursive-path reduction ordering.

This function converts a :any:`ToddCoxeter` object *tc* to a :any:`KnuthBendix`
object with the rewriter as specified above, using
Expand Down Expand Up @@ -186,6 +188,18 @@ Additionally, specify one of the following for *rtype*:
- ``(KnuthBendix, list[int], 'Set', Order.rpo)`` for constructing a
:any:`KnuthBendix` on words with type ``list[int]`` using a set based
rewriting system and short-lex reduction ordering.
- ``(KnuthBendix, str, 'Trie', Order.rev_rpo)`` for constructing a
:any:`KnuthBendix` on words with type ``str`` using the
trie based rewriting system and reverse recursive-path reduction ordering.
- ``(KnuthBendix, list[int], 'Trie', Order.rev_rpo)`` for constructing a
:any:`KnuthBendix` on words with type ``list[int]`` using the
trie based rewriting system and reverse recursive-path reduction ordering.
- ``(KnuthBendix, str, 'Set', Order.rev_rpo)`` for constructing a
:any:`KnuthBendix` on words with type ``str`` using a set based rewriting
system and reverse recursive-path reduction ordering.
- ``(KnuthBendix, list[int], 'Set', Order.rev_rpo)`` for constructing a
:any:`KnuthBendix` on words with type ``list[int]`` using a set based
rewriting system and reverse recursive-path reduction.

This function converts a :any:`FroidurePin` object *fpb* to a :any:`KnuthBendix`
object with the word type and rewriter as specified above. This is done using
Expand Down
130 changes: 130 additions & 0 deletions src/cong-common.cpp
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Expand Up @@ -42,6 +42,8 @@ namespace libsemigroups {

using LenLexTrie = detail::RewritingSystemTrie<LenLexCmp>;
using LenLexSet = detail::RewritingSystemSet<LenLexCmp>;
using RPOTrie = detail::RewritingSystemTrie<RPOCmp>;
using RPOSet = detail::RewritingSystemSet<RPOCmp>;
using RevRPOTrie = detail::RewritingSystemTrie<RevRPOCmp>;
using RevRPOSet = detail::RewritingSystemSet<RevRPOCmp>;

Expand All @@ -54,6 +56,11 @@ namespace libsemigroups {
using KnuthBendixWordLenLexTrie = KnuthBendix<word_type, LenLexTrie>;
using KnuthBendixWordLenLexSet = KnuthBendix<word_type, LenLexSet>;

using KnuthBendixStringRPOTrie = KnuthBendix<std::string, RPOTrie>;
using KnuthBendixStringRPOSet = KnuthBendix<std::string, RPOSet>;
using KnuthBendixWordRPOTrie = KnuthBendix<word_type, RPOTrie>;
using KnuthBendixWordRPOSet = KnuthBendix<word_type, RPOSet>;

using KnuthBendixStringRevRPOTrie = KnuthBendix<std::string, RevRPOTrie>;
using KnuthBendixStringRevRPOSet = KnuthBendix<std::string, RevRPOSet>;
using KnuthBendixWordRevRPOTrie = KnuthBendix<word_type, RevRPOTrie>;
Expand Down Expand Up @@ -138,6 +145,11 @@ This function default constructs an uninitialised :any:`{name}` instance.
DEF_CONSTRUCT_DEFAULT(detail::KnuthBendixImpl<LenLexSet>,
detail::CongruenceCommon);

DEF_CONSTRUCT_DEFAULT(detail::KnuthBendixImpl<RPOTrie>,
detail::CongruenceCommon);
DEF_CONSTRUCT_DEFAULT(detail::KnuthBendixImpl<RPOSet>,
detail::CongruenceCommon);

DEF_CONSTRUCT_DEFAULT(detail::KnuthBendixImpl<RevRPOTrie>,
detail::CongruenceCommon);
DEF_CONSTRUCT_DEFAULT(detail::KnuthBendixImpl<RevRPOSet>,
Expand All @@ -152,6 +164,14 @@ This function default constructs an uninitialised :any:`{name}` instance.
DEF_CONSTRUCT_DEFAULT(KnuthBendixWordLenLexSet,
detail::KnuthBendixImpl<LenLexSet>);

DEF_CONSTRUCT_DEFAULT(KnuthBendixStringRPOTrie,
detail::KnuthBendixImpl<RPOTrie>);
DEF_CONSTRUCT_DEFAULT(KnuthBendixStringRPOSet,
detail::KnuthBendixImpl<RPOSet>);
DEF_CONSTRUCT_DEFAULT(KnuthBendixWordRPOTrie,
detail::KnuthBendixImpl<RPOTrie>);
DEF_CONSTRUCT_DEFAULT(KnuthBendixWordRPOSet, detail::KnuthBendixImpl<RPOSet>);

DEF_CONSTRUCT_DEFAULT(KnuthBendixStringRevRPOTrie,
detail::KnuthBendixImpl<RevRPOTrie>);
DEF_CONSTRUCT_DEFAULT(KnuthBendixStringRevRPOSet,
Expand Down Expand Up @@ -212,6 +232,9 @@ have been in if it had just been newly default constructed.
DEF_INIT_DEFAULT(detail::KnuthBendixImpl<LenLexSet>,
detail::CongruenceCommon);

DEF_INIT_DEFAULT(detail::KnuthBendixImpl<RPOTrie>, detail::CongruenceCommon);
DEF_INIT_DEFAULT(detail::KnuthBendixImpl<RPOSet>, detail::CongruenceCommon);

DEF_INIT_DEFAULT(detail::KnuthBendixImpl<RevRPOTrie>,
detail::CongruenceCommon);
DEF_INIT_DEFAULT(detail::KnuthBendixImpl<RevRPOSet>,
Expand All @@ -226,6 +249,11 @@ have been in if it had just been newly default constructed.
DEF_INIT_DEFAULT(KnuthBendixWordLenLexSet,
detail::KnuthBendixImpl<LenLexSet>);

DEF_INIT_DEFAULT(KnuthBendixStringRPOTrie, detail::KnuthBendixImpl<RPOTrie>);
DEF_INIT_DEFAULT(KnuthBendixStringRPOSet, detail::KnuthBendixImpl<RPOSet>);
DEF_INIT_DEFAULT(KnuthBendixWordRPOTrie, detail::KnuthBendixImpl<RPOTrie>);
DEF_INIT_DEFAULT(KnuthBendixWordRPOSet, detail::KnuthBendixImpl<RPOSet>);

DEF_INIT_DEFAULT(KnuthBendixStringRevRPOTrie,
detail::KnuthBendixImpl<RevRPOTrie>);
DEF_INIT_DEFAULT(KnuthBendixStringRevRPOSet,
Expand Down Expand Up @@ -309,11 +337,25 @@ of kind *knd* over the semigroup or monoid defined by the presentation *p*.
DEF_CONSTRUCT_KIND_PRESENTATION(KnuthBendixWordLenLexSet,
detail::KnuthBendixImpl<LenLexSet>);

DEF_CONSTRUCT_KIND_PRESENTATION(detail::KnuthBendixImpl<RPOTrie>,
detail::CongruenceCommon);
DEF_CONSTRUCT_KIND_PRESENTATION(detail::KnuthBendixImpl<RPOSet>,
detail::CongruenceCommon);

DEF_CONSTRUCT_KIND_PRESENTATION(detail::KnuthBendixImpl<RevRPOTrie>,
detail::CongruenceCommon);
DEF_CONSTRUCT_KIND_PRESENTATION(detail::KnuthBendixImpl<RevRPOSet>,
detail::CongruenceCommon);

DEF_CONSTRUCT_KIND_PRESENTATION(KnuthBendixStringRPOTrie,
detail::KnuthBendixImpl<RPOTrie>);
DEF_CONSTRUCT_KIND_PRESENTATION(KnuthBendixStringRPOSet,
detail::KnuthBendixImpl<RPOSet>);
DEF_CONSTRUCT_KIND_PRESENTATION(KnuthBendixWordRPOTrie,
detail::KnuthBendixImpl<RPOTrie>);
DEF_CONSTRUCT_KIND_PRESENTATION(KnuthBendixWordRPOSet,
detail::KnuthBendixImpl<RPOSet>);

DEF_CONSTRUCT_KIND_PRESENTATION(KnuthBendixStringRevRPOTrie,
detail::KnuthBendixImpl<RevRPOTrie>);
DEF_CONSTRUCT_KIND_PRESENTATION(KnuthBendixStringRevRPOSet,
Expand Down Expand Up @@ -400,11 +442,25 @@ had been newly constructed from *knd* and *p*.
DEF_INIT_KIND_PRESENTATION(KnuthBendixWordLenLexSet,
detail::KnuthBendixImpl<LenLexSet>);

DEF_INIT_KIND_PRESENTATION(detail::KnuthBendixImpl<RPOTrie>,
detail::CongruenceCommon);
DEF_INIT_KIND_PRESENTATION(detail::KnuthBendixImpl<RPOSet>,
detail::CongruenceCommon);

DEF_INIT_KIND_PRESENTATION(detail::KnuthBendixImpl<RevRPOTrie>,
detail::CongruenceCommon);
DEF_INIT_KIND_PRESENTATION(detail::KnuthBendixImpl<RevRPOSet>,
detail::CongruenceCommon);

DEF_INIT_KIND_PRESENTATION(KnuthBendixStringRPOTrie,
detail::KnuthBendixImpl<RPOTrie>);
DEF_INIT_KIND_PRESENTATION(KnuthBendixStringRPOSet,
detail::KnuthBendixImpl<RPOSet>);
DEF_INIT_KIND_PRESENTATION(KnuthBendixWordRPOTrie,
detail::KnuthBendixImpl<RPOTrie>);
DEF_INIT_KIND_PRESENTATION(KnuthBendixWordRPOSet,
detail::KnuthBendixImpl<RPOSet>);

DEF_INIT_KIND_PRESENTATION(KnuthBendixStringRevRPOTrie,
detail::KnuthBendixImpl<RevRPOTrie>);
DEF_INIT_KIND_PRESENTATION(KnuthBendixStringRevRPOSet,
Expand Down Expand Up @@ -465,9 +521,17 @@ Copy a :any:`{name}` object.
DEF_COPY(KnuthBendixWordLenLexTrie, detail::KnuthBendixImpl<LenLexTrie>);
DEF_COPY(KnuthBendixWordLenLexSet, detail::KnuthBendixImpl<LenLexSet>);

DEF_COPY(detail::KnuthBendixImpl<RPOTrie>, detail::CongruenceCommon);
DEF_COPY(detail::KnuthBendixImpl<RPOSet>, detail::CongruenceCommon);

DEF_COPY(detail::KnuthBendixImpl<RevRPOTrie>, detail::CongruenceCommon);
DEF_COPY(detail::KnuthBendixImpl<RevRPOSet>, detail::CongruenceCommon);

DEF_COPY(KnuthBendixStringRPOTrie, detail::KnuthBendixImpl<RPOTrie>);
DEF_COPY(KnuthBendixStringRPOSet, detail::KnuthBendixImpl<RPOSet>);
DEF_COPY(KnuthBendixWordRPOTrie, detail::KnuthBendixImpl<RPOTrie>);
DEF_COPY(KnuthBendixWordRPOSet, detail::KnuthBendixImpl<RPOSet>);

DEF_COPY(KnuthBendixStringRevRPOTrie, detail::KnuthBendixImpl<RevRPOTrie>);
DEF_COPY(KnuthBendixStringRevRPOSet, detail::KnuthBendixImpl<RevRPOSet>);
DEF_COPY(KnuthBendixWordRevRPOTrie, detail::KnuthBendixImpl<RevRPOTrie>);
Expand Down Expand Up @@ -529,6 +593,11 @@ number of classes in the congruence represented by a :any:`{name}` instance.
DEF_NUMBER_OF_CLASSES(detail::KnuthBendixImpl<LenLexSet>,
detail::CongruenceCommon);

DEF_NUMBER_OF_CLASSES(detail::KnuthBendixImpl<RPOTrie>,
detail::CongruenceCommon);
DEF_NUMBER_OF_CLASSES(detail::KnuthBendixImpl<RPOSet>,
detail::CongruenceCommon);

DEF_NUMBER_OF_CLASSES(detail::KnuthBendixImpl<RevRPOTrie>,
detail::CongruenceCommon);
DEF_NUMBER_OF_CLASSES(detail::KnuthBendixImpl<RevRPOSet>,
Expand Down Expand Up @@ -610,6 +679,15 @@ This function adds a generating pair to the congruence represented by a
DEF_ADD_GENERATING_PAIR(KnuthBendixWordLenLexSet,
detail::KnuthBendixImpl<LenLexSet>);

DEF_ADD_GENERATING_PAIR(KnuthBendixStringRPOTrie,
detail::KnuthBendixImpl<RPOTrie>);
DEF_ADD_GENERATING_PAIR(KnuthBendixStringRPOSet,
detail::KnuthBendixImpl<RPOSet>);
DEF_ADD_GENERATING_PAIR(KnuthBendixWordRPOTrie,
detail::KnuthBendixImpl<RPOTrie>);
DEF_ADD_GENERATING_PAIR(KnuthBendixWordRPOSet,
detail::KnuthBendixImpl<RPOSet>);

DEF_ADD_GENERATING_PAIR(KnuthBendixStringRevRPOTrie,
detail::KnuthBendixImpl<RevRPOTrie>);
DEF_ADD_GENERATING_PAIR(KnuthBendixStringRevRPOSet,
Expand Down Expand Up @@ -695,6 +773,15 @@ contained in the congruence, but that this is not currently known.
DEF_CURRENTLY_CONTAINS(KnuthBendixWordLenLexSet,
detail::KnuthBendixImpl<LenLexSet>);

DEF_CURRENTLY_CONTAINS(KnuthBendixStringRPOTrie,
detail::KnuthBendixImpl<RPOTrie>);
DEF_CURRENTLY_CONTAINS(KnuthBendixStringRPOSet,
detail::KnuthBendixImpl<RPOSet>);
DEF_CURRENTLY_CONTAINS(KnuthBendixWordRPOTrie,
detail::KnuthBendixImpl<RPOTrie>);
DEF_CURRENTLY_CONTAINS(KnuthBendixWordRPOSet,
detail::KnuthBendixImpl<RPOSet>);

DEF_CURRENTLY_CONTAINS(KnuthBendixStringRevRPOTrie,
detail::KnuthBendixImpl<RevRPOTrie>);
DEF_CURRENTLY_CONTAINS(KnuthBendixStringRevRPOSet,
Expand Down Expand Up @@ -770,6 +857,11 @@ congruence represented by a :py:class:`{name}` instance.
DEF_CONTAINS(KnuthBendixWordLenLexTrie, detail::KnuthBendixImpl<LenLexTrie>);
DEF_CONTAINS(KnuthBendixWordLenLexSet, detail::KnuthBendixImpl<LenLexSet>);

DEF_CONTAINS(KnuthBendixStringRPOTrie, detail::KnuthBendixImpl<RPOTrie>);
DEF_CONTAINS(KnuthBendixStringRPOSet, detail::KnuthBendixImpl<RPOSet>);
DEF_CONTAINS(KnuthBendixWordRPOTrie, detail::KnuthBendixImpl<RPOTrie>);
DEF_CONTAINS(KnuthBendixWordRPOSet, detail::KnuthBendixImpl<RPOSet>);

DEF_CONTAINS(KnuthBendixStringRevRPOTrie,
detail::KnuthBendixImpl<RevRPOTrie>);
DEF_CONTAINS(KnuthBendixStringRevRPOSet, detail::KnuthBendixImpl<RevRPOSet>);
Expand Down Expand Up @@ -842,6 +934,11 @@ normal form for the input word *w*.
DEF_REDUCE_NO_RUN(KnuthBendixWordLenLexSet,
detail::KnuthBendixImpl<LenLexSet>);

DEF_REDUCE_NO_RUN(KnuthBendixStringRPOTrie, detail::KnuthBendixImpl<RPOTrie>);
DEF_REDUCE_NO_RUN(KnuthBendixStringRPOSet, detail::KnuthBendixImpl<RPOSet>);
DEF_REDUCE_NO_RUN(KnuthBendixWordRPOTrie, detail::KnuthBendixImpl<RPOTrie>);
DEF_REDUCE_NO_RUN(KnuthBendixWordRPOSet, detail::KnuthBendixImpl<RPOSet>);

DEF_REDUCE_NO_RUN(KnuthBendixStringRevRPOTrie,
detail::KnuthBendixImpl<RevRPOTrie>);
DEF_REDUCE_NO_RUN(KnuthBendixStringRevRPOSet,
Expand Down Expand Up @@ -914,6 +1011,11 @@ input word.
DEF_REDUCE(KnuthBendixWordLenLexTrie, detail::KnuthBendixImpl<LenLexTrie>);
DEF_REDUCE(KnuthBendixWordLenLexSet, detail::KnuthBendixImpl<LenLexSet>);

DEF_REDUCE(KnuthBendixStringRPOTrie, detail::KnuthBendixImpl<RPOTrie>);
DEF_REDUCE(KnuthBendixStringRPOSet, detail::KnuthBendixImpl<RPOSet>);
DEF_REDUCE(KnuthBendixWordRPOTrie, detail::KnuthBendixImpl<RPOTrie>);
DEF_REDUCE(KnuthBendixWordRPOSet, detail::KnuthBendixImpl<RPOSet>);

DEF_REDUCE(KnuthBendixStringRevRPOTrie, detail::KnuthBendixImpl<RevRPOTrie>);
DEF_REDUCE(KnuthBendixStringRevRPOSet, detail::KnuthBendixImpl<RevRPOSet>);
DEF_REDUCE(KnuthBendixWordRevRPOTrie, detail::KnuthBendixImpl<RevRPOTrie>);
Expand Down Expand Up @@ -977,6 +1079,14 @@ This function returns the generating pairs of the congruence as added via
DEF_GENERATING_PAIRS(KnuthBendixWordLenLexSet,
detail::KnuthBendixImpl<LenLexSet>);

DEF_GENERATING_PAIRS(KnuthBendixStringRPOTrie,
detail::KnuthBendixImpl<RPOTrie>);
DEF_GENERATING_PAIRS(KnuthBendixStringRPOSet,
detail::KnuthBendixImpl<RPOSet>);
DEF_GENERATING_PAIRS(KnuthBendixWordRPOTrie,
detail::KnuthBendixImpl<RPOTrie>);
DEF_GENERATING_PAIRS(KnuthBendixWordRPOSet, detail::KnuthBendixImpl<RPOSet>);

DEF_GENERATING_PAIRS(KnuthBendixStringRevRPOTrie,
detail::KnuthBendixImpl<RevRPOTrie>);
DEF_GENERATING_PAIRS(KnuthBendixStringRevRPOSet,
Expand Down Expand Up @@ -1045,6 +1155,11 @@ presentation, then this presentation is returned by this function.
DEF_PRESENTATION(KnuthBendixWordLenLexSet,
detail::KnuthBendixImpl<LenLexSet>);

DEF_PRESENTATION(KnuthBendixStringRPOTrie, detail::KnuthBendixImpl<RPOTrie>);
DEF_PRESENTATION(KnuthBendixStringRPOSet, detail::KnuthBendixImpl<RPOSet>);
DEF_PRESENTATION(KnuthBendixWordRPOTrie, detail::KnuthBendixImpl<RPOTrie>);
DEF_PRESENTATION(KnuthBendixWordRPOSet, detail::KnuthBendixImpl<RPOSet>);

DEF_PRESENTATION(KnuthBendixStringRevRPOTrie,
detail::KnuthBendixImpl<RevRPOTrie>);
DEF_PRESENTATION(KnuthBendixStringRevRPOSet,
Expand Down Expand Up @@ -1122,6 +1237,11 @@ triggers a full enumeration of *{var}*.
DEF_PARTITION(KnuthBendixWordLenLexTrie);
DEF_PARTITION(KnuthBendixWordLenLexSet);

DEF_PARTITION(KnuthBendixStringRPOTrie);
DEF_PARTITION(KnuthBendixStringRPOSet);
DEF_PARTITION(KnuthBendixWordRPOTrie);
DEF_PARTITION(KnuthBendixWordRPOSet);

DEF_PARTITION(KnuthBendixStringRevRPOTrie);
DEF_PARTITION(KnuthBendixStringRevRPOSet);
DEF_PARTITION(KnuthBendixWordRevRPOTrie);
Expand Down Expand Up @@ -1194,6 +1314,11 @@ instance *{var}*.
DEF_NON_TRIVIAL_CLASSES(KnuthBendixWordLenLexTrie);
DEF_NON_TRIVIAL_CLASSES(KnuthBendixWordLenLexSet);

DEF_NON_TRIVIAL_CLASSES(KnuthBendixStringRPOTrie);
DEF_NON_TRIVIAL_CLASSES(KnuthBendixStringRPOSet);
DEF_NON_TRIVIAL_CLASSES(KnuthBendixWordRPOTrie);
DEF_NON_TRIVIAL_CLASSES(KnuthBendixWordRPOSet);

DEF_NON_TRIVIAL_CLASSES(KnuthBendixStringRevRPOTrie);
DEF_NON_TRIVIAL_CLASSES(KnuthBendixStringRevRPOSet);
DEF_NON_TRIVIAL_CLASSES(KnuthBendixWordRevRPOTrie);
Expand Down Expand Up @@ -1262,6 +1387,11 @@ the congruence represented by an instance of :any:`{name}`.
DEF_NORMAL_FORMS(KnuthBendixWordLenLexTrie);
DEF_NORMAL_FORMS(KnuthBendixWordLenLexSet);

DEF_NORMAL_FORMS(KnuthBendixStringRPOTrie);
DEF_NORMAL_FORMS(KnuthBendixStringRPOSet);
DEF_NORMAL_FORMS(KnuthBendixWordRPOTrie);
DEF_NORMAL_FORMS(KnuthBendixWordRPOSet);

DEF_NORMAL_FORMS(KnuthBendixStringRevRPOTrie);
DEF_NORMAL_FORMS(KnuthBendixStringRevRPOSet);
DEF_NORMAL_FORMS(KnuthBendixWordRevRPOTrie);
Expand Down
18 changes: 10 additions & 8 deletions src/du-narendran-rusinowitch.cpp
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Expand Up @@ -46,24 +46,26 @@ namespace libsemigroups {
R"pbdoc(
:sig=(p: Presentation) -> str | list[int]:
:only-document-once:
Find an alphabet order that orients every rule using reverse recursive-path ordering.
Return an ordered alphabet such that the rules are oriented with
respect to recursive-path order; see :any:`rpo_cmp`.

This function returns the alphabet of *p*, ordered so that every rule
:math:`u \to v` satisfies :math:`u > v` with respect to reverse recursive-path
ordering. It returns an empty word if no such order exists, or if the alphabet
of *p* is empty.
This function returns the alphabet of *p* ordered so that the rules of
*p* satisfy :math:`x_i \to y_i` and :math`x_i > y_i` with respect to
recursive-path order and the returned alphabet order. The returned
alphabet is empty if this fails, or if the alphabet was empty to begin
with.

:param p: the presentation whose rules are to be oriented.
:type p: Presentation

:returns: An alphabet order orienting every rule, or an empty word if none
exists.
:returns: The ordered alphabet, if such an alphabet exists. Otherwise, the
empty alphabet.

@james-d-mitchell james-d-mitchell Aug 28, 2026

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This isn't really a comment about this PR, but maybe this should return None if it can't do it.

@Joseph-Edwards Joseph-Edwards Aug 28, 2026

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Do you think we should change the C++ code to return an optional, or should this be a Python only change?

:rtype: str | list[int]

:raises LibsemigroupsError: if the alphabet or rules of *p* are invalid.

.. seealso::
:any:`rev_rpo_cmp`
:any:`rpo_cmp`

.. doctest::

Expand Down
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