diff --git a/src/cong-common.cpp b/src/cong-common.cpp
index 590c2206..94870ab5 100644
--- a/src/cong-common.cpp
+++ b/src/cong-common.cpp
@@ -593,8 +593,6 @@ This function adds a generating pair to the congruence represented by a
   template void def_add_generating_pair<A, B>( \
       py::class_<A, B>&, std::string_view, doc)
 
-  DEF_ADD_GENERATING_PAIR(detail::ToddCoxeterImpl, detail::CongruenceCommon);
-
   DEF_ADD_GENERATING_PAIR(ToddCoxeter<word_type>, detail::ToddCoxeterImpl);
   DEF_ADD_GENERATING_PAIR(ToddCoxeter<std::string>, detail::ToddCoxeterImpl);
 
@@ -603,11 +601,6 @@ This function adds a generating pair to the congruence represented by a
                           detail::CongruenceCommon);
   DEF_ADD_GENERATING_PAIR(Kambites<std::string>, detail::CongruenceCommon);
 
-  DEF_ADD_GENERATING_PAIR(detail::KnuthBendixImpl<LenLexTrie>,
-                          detail::CongruenceCommon);
-  DEF_ADD_GENERATING_PAIR(detail::KnuthBendixImpl<LenLexSet>,
-                          detail::CongruenceCommon);
-
   DEF_ADD_GENERATING_PAIR(KnuthBendixStringLenLexTrie,
                           detail::KnuthBendixImpl<LenLexTrie>);
   DEF_ADD_GENERATING_PAIR(KnuthBendixStringLenLexSet,
@@ -617,11 +610,6 @@ This function adds a generating pair to the congruence represented by a
   DEF_ADD_GENERATING_PAIR(KnuthBendixWordLenLexSet,
                           detail::KnuthBendixImpl<LenLexSet>);
 
-  DEF_ADD_GENERATING_PAIR(detail::KnuthBendixImpl<RevRPOTrie>,
-                          detail::CongruenceCommon);
-  DEF_ADD_GENERATING_PAIR(detail::KnuthBendixImpl<RevRPOSet>,
-                          detail::CongruenceCommon);
-
   DEF_ADD_GENERATING_PAIR(KnuthBendixStringRevRPOTrie,
                           detail::KnuthBendixImpl<RevRPOTrie>);
   DEF_ADD_GENERATING_PAIR(KnuthBendixStringRevRPOSet,
@@ -690,8 +678,6 @@ contained in the congruence, but that this is not currently known.
   template void def_currently_contains<A, B>( \
       py::class_<A, B>&, std::string_view, doc)
 
-  DEF_CURRENTLY_CONTAINS(detail::ToddCoxeterImpl, detail::CongruenceCommon);
-
   DEF_CURRENTLY_CONTAINS(ToddCoxeter<word_type>, detail::ToddCoxeterImpl);
   DEF_CURRENTLY_CONTAINS(ToddCoxeter<std::string>, detail::ToddCoxeterImpl);
 
@@ -700,11 +686,6 @@ contained in the congruence, but that this is not currently known.
                          detail::CongruenceCommon);
   DEF_CURRENTLY_CONTAINS(Kambites<std::string>, detail::CongruenceCommon);
 
-  DEF_CURRENTLY_CONTAINS(detail::KnuthBendixImpl<LenLexTrie>,
-                         detail::CongruenceCommon);
-  DEF_CURRENTLY_CONTAINS(detail::KnuthBendixImpl<LenLexSet>,
-                         detail::CongruenceCommon);
-
   DEF_CURRENTLY_CONTAINS(KnuthBendixStringLenLexTrie,
                          detail::KnuthBendixImpl<LenLexTrie>);
   DEF_CURRENTLY_CONTAINS(KnuthBendixStringLenLexSet,
@@ -714,11 +695,6 @@ contained in the congruence, but that this is not currently known.
   DEF_CURRENTLY_CONTAINS(KnuthBendixWordLenLexSet,
                          detail::KnuthBendixImpl<LenLexSet>);
 
-  DEF_CURRENTLY_CONTAINS(detail::KnuthBendixImpl<RevRPOTrie>,
-                         detail::CongruenceCommon);
-  DEF_CURRENTLY_CONTAINS(detail::KnuthBendixImpl<RevRPOSet>,
-                         detail::CongruenceCommon);
-
   DEF_CURRENTLY_CONTAINS(KnuthBendixStringRevRPOTrie,
                          detail::KnuthBendixImpl<RevRPOTrie>);
   DEF_CURRENTLY_CONTAINS(KnuthBendixStringRevRPOSet,
@@ -781,8 +757,6 @@ congruence represented by a :py:class:`{name}` instance.
 #define DEF_CONTAINS(A, B) \
   template void def_contains<A, B>(py::class_<A, B>&, std::string_view, doc)
 
-  DEF_CONTAINS(detail::ToddCoxeterImpl, detail::CongruenceCommon);
-
   DEF_CONTAINS(ToddCoxeter<word_type>, detail::ToddCoxeterImpl);
   DEF_CONTAINS(ToddCoxeter<std::string>, detail::ToddCoxeterImpl);
 
@@ -790,18 +764,12 @@ congruence represented by a :py:class:`{name}` instance.
   DEF_CONTAINS(Kambites<MultiView<std::string>>, detail::CongruenceCommon);
   DEF_CONTAINS(Kambites<std::string>, detail::CongruenceCommon);
 
-  DEF_CONTAINS(detail::KnuthBendixImpl<LenLexTrie>, detail::CongruenceCommon);
-  DEF_CONTAINS(detail::KnuthBendixImpl<LenLexSet>, detail::CongruenceCommon);
-
   DEF_CONTAINS(KnuthBendixStringLenLexTrie,
                detail::KnuthBendixImpl<LenLexTrie>);
   DEF_CONTAINS(KnuthBendixStringLenLexSet, detail::KnuthBendixImpl<LenLexSet>);
   DEF_CONTAINS(KnuthBendixWordLenLexTrie, detail::KnuthBendixImpl<LenLexTrie>);
   DEF_CONTAINS(KnuthBendixWordLenLexSet, detail::KnuthBendixImpl<LenLexSet>);
 
-  DEF_CONTAINS(detail::KnuthBendixImpl<RevRPOTrie>, detail::CongruenceCommon);
-  DEF_CONTAINS(detail::KnuthBendixImpl<RevRPOSet>, detail::CongruenceCommon);
-
   DEF_CONTAINS(KnuthBendixStringRevRPOTrie,
                detail::KnuthBendixImpl<RevRPOTrie>);
   DEF_CONTAINS(KnuthBendixStringRevRPOSet, detail::KnuthBendixImpl<RevRPOSet>);
@@ -858,8 +826,6 @@ normal form for the input word *w*.
   template void def_reduce_no_run<A, B>( \
       py::class_<A, B>&, std::string_view, doc)
 
-  DEF_REDUCE_NO_RUN(detail::ToddCoxeterImpl, detail::CongruenceCommon);
-
   DEF_REDUCE_NO_RUN(ToddCoxeter<word_type>, detail::ToddCoxeterImpl);
   DEF_REDUCE_NO_RUN(ToddCoxeter<std::string>, detail::ToddCoxeterImpl);
 
@@ -867,11 +833,6 @@ normal form for the input word *w*.
   DEF_REDUCE_NO_RUN(Kambites<MultiView<std::string>>, detail::CongruenceCommon);
   DEF_REDUCE_NO_RUN(Kambites<std::string>, detail::CongruenceCommon);
 
-  DEF_REDUCE_NO_RUN(detail::KnuthBendixImpl<LenLexTrie>,
-                    detail::CongruenceCommon);
-  DEF_REDUCE_NO_RUN(detail::KnuthBendixImpl<LenLexSet>,
-                    detail::CongruenceCommon);
-
   DEF_REDUCE_NO_RUN(KnuthBendixStringLenLexTrie,
                     detail::KnuthBendixImpl<LenLexTrie>);
   DEF_REDUCE_NO_RUN(KnuthBendixStringLenLexSet,
@@ -881,11 +842,6 @@ normal form for the input word *w*.
   DEF_REDUCE_NO_RUN(KnuthBendixWordLenLexSet,
                     detail::KnuthBendixImpl<LenLexSet>);
 
-  DEF_REDUCE_NO_RUN(detail::KnuthBendixImpl<RevRPOTrie>,
-                    detail::CongruenceCommon);
-  DEF_REDUCE_NO_RUN(detail::KnuthBendixImpl<RevRPOSet>,
-                    detail::CongruenceCommon);
-
   DEF_REDUCE_NO_RUN(KnuthBendixStringRevRPOTrie,
                     detail::KnuthBendixImpl<RevRPOTrie>);
   DEF_REDUCE_NO_RUN(KnuthBendixStringRevRPOSet,
@@ -946,8 +902,6 @@ input word.
 #define DEF_REDUCE(A, B) \
   template void def_reduce<A, B>(py::class_<A, B>&, std::string_view, doc)
 
-  DEF_REDUCE(detail::ToddCoxeterImpl, detail::CongruenceCommon);
-
   DEF_REDUCE(ToddCoxeter<word_type>, detail::ToddCoxeterImpl);
   DEF_REDUCE(ToddCoxeter<std::string>, detail::ToddCoxeterImpl);
 
@@ -955,17 +909,11 @@ input word.
   DEF_REDUCE(Kambites<MultiView<std::string>>, detail::CongruenceCommon);
   DEF_REDUCE(Kambites<std::string>, detail::CongruenceCommon);
 
-  DEF_REDUCE(detail::KnuthBendixImpl<LenLexTrie>, detail::CongruenceCommon);
-  DEF_REDUCE(detail::KnuthBendixImpl<LenLexSet>, detail::CongruenceCommon);
-
   DEF_REDUCE(KnuthBendixStringLenLexTrie, detail::KnuthBendixImpl<LenLexTrie>);
   DEF_REDUCE(KnuthBendixStringLenLexSet, detail::KnuthBendixImpl<LenLexSet>);
   DEF_REDUCE(KnuthBendixWordLenLexTrie, detail::KnuthBendixImpl<LenLexTrie>);
   DEF_REDUCE(KnuthBendixWordLenLexSet, detail::KnuthBendixImpl<LenLexSet>);
 
-  DEF_REDUCE(detail::KnuthBendixImpl<RevRPOTrie>, detail::CongruenceCommon);
-  DEF_REDUCE(detail::KnuthBendixImpl<RevRPOSet>, detail::CongruenceCommon);
-
   DEF_REDUCE(KnuthBendixStringRevRPOTrie, detail::KnuthBendixImpl<RevRPOTrie>);
   DEF_REDUCE(KnuthBendixStringRevRPOSet, detail::KnuthBendixImpl<RevRPOSet>);
   DEF_REDUCE(KnuthBendixWordRevRPOTrie, detail::KnuthBendixImpl<RevRPOTrie>);
diff --git a/src/knuth-bendix-impl.cpp b/src/knuth-bendix-impl.cpp
index c4a04b8a..16bb2d11 100644
--- a/src/knuth-bendix-impl.cpp
+++ b/src/knuth-bendix-impl.cpp
@@ -118,11 +118,6 @@ The valid values are:
       def_copy(thing, "KnuthBendix");
       // The next function has a reference hence the different "KnuthBendix".
       def_number_of_classes(thing, "KnuthBendix");
-      def_add_generating_pair(thing, "KnuthBendix");
-      def_contains(thing, "KnuthBendix");
-      def_currently_contains(thing, "KnuthBendix");
-      def_reduce_no_run(thing, "KnuthBendix");
-      def_reduce(thing, "KnuthBendix");
 
       // Not exposed in the doc
       thing.def("internal_presentation",
diff --git a/src/todd-coxeter-impl.cpp b/src/todd-coxeter-impl.cpp
index 3c4dc5fb..cd392df2 100644
--- a/src/todd-coxeter-impl.cpp
+++ b/src/todd-coxeter-impl.cpp
@@ -260,14 +260,7 @@ The valid values are:
     def_init_kind_presentation(thing, "ToddCoxeterImpl_");
     def_number_of_classes(thing, "ToddCoxeter");
     def_copy(thing, "ToddCoxeterImpl_");
-    def_add_generating_pair(thing, "ToddCoxeterImpl_");
-    def_currently_contains(thing, "ToddCoxeterImpl_");
-    def_contains(thing, "ToddCoxeterImpl_");
-    def_reduce_no_run(thing, "ToddCoxeterImpl_", doc{.detail = R"pbdoc(
-If the :any:`ToddCoxeter` instance is not :any:`Runner.finished`,
-then it might be that equivalent input words produce different output
-words. This function triggers no congruence enumeration.)pbdoc"sv});
-    def_reduce(thing, "ToddCoxeterImpl_");
+
     // There's no generating_pairs for ToddCoxeterImpl_ only
     // internal_generating_pairs