| Σ | # | Presentation | Description | Related |
|---|
| 6 | 62 | ⟨a, b | ab=a, ba=a⟩ | Infinite non-cancellative commutative monoid | 34 iso |
| 7 | 162 | ⟨a, b | ba=ab, bb=b⟩ | Isomorphic to ℕ(2 = 1) ⊕ ℕ | 8 iso |
| 7 | 240 | ⟨a, b | aa=a, aba=b⟩ | Infinite non-cancellative commutative monoid | 8 iso |
| 7 | 243 | ⟨a, b | aa=a, bab=a⟩ | Infinite non-cancellative commutative monoid | 100 iso |
| 7 | 267 | ⟨a, b | ab=a, baa=a⟩ | Infinite non-cancellative commutative monoid | 168 iso |
| 8 | 566 | ⟨a, b | aaa=a, aba=b⟩ | Infinite non-cancellative commutative monoid | 1 iso |
| 8 | 586 | ⟨a, b | aab=a, baa=a⟩ | Infinite non-cancellative commutative monoid | 14 iso |
| 8 | 588 | ⟨a, b | aab=a, bab=a⟩ | Infinite non-cancellative commutative monoid | 41 iso |
| 8 | 593 | ⟨a, b | aab=b, aba=b⟩ | Infinite non-cancellative commutative monoid | 10 iso |
| 8 | 646 | ⟨a, b | ba=ab, aaa=a⟩ | Isomorphic to ℕ(3 = 1) ⊕ ℕ | 1 iso |
| 8 | 658 | ⟨a, b | ab=aa, ba=aa⟩ | Infinite non-cancellative commutative monoid | 1 iso |
| 8 | 936 | ⟨a, b | ab=a, baaa=a⟩ | Infinite non-cancellative commutative monoid | 55 iso |
| 9 | 1579 | ⟨a, b | aaa=aa, aba=b⟩ | Infinite non-cancellative commutative monoid | 3 iso |
| 9 | 1592 | ⟨a, b | aaa=ab, baa=a⟩ | Infinite non-cancellative commutative monoid | 39 iso |
| 9 | 1594 | ⟨a, b | aaa=ab, bab=a⟩ | Infinite non-cancellative commutative monoid | 26 iso |
| 9 | 1685 | ⟨a, b | aba=bb, bbb=b⟩ | Infinite non-cancellative commutative monoid | 25 iso |
| 9 | 2123 | ⟨a, b | aba=b, bbbb=b⟩ | Infinite non-cancellative commutative monoid | 17 iso |
| 9 | 2192 | ⟨a, b | ab=aa, baaa=a⟩ | Infinite non-cancellative commutative monoid | 28 iso |
| 9 | 2208 | ⟨a, b | ba=ab, aaaa=a⟩ | Isomorphic to ℕ(4 = 1) ⊕ ℕ | 1 iso |
| 9 | 2210 | ⟨a, b | ba=ab, aaab=a⟩ | Infinite non-cancellative commutative monoid | 5 iso |
| 9 | 2211 | ⟨a, b | ba=ab, aaab=b⟩ | Infinite non-cancellative commutative monoid | 6 iso |
| 9 | 2214 | ⟨a, b | ba=ab, aabb=a⟩ | Infinite non-cancellative commutative monoid | 15 iso |
| 9 | 2260 | ⟨a, b | ba=ab, aaa=aa⟩ | Isomorphic to ℕ(3 = 2) ⊕ ℕ | |
| 9 | 2261 | ⟨a, b | ba=ab, aaa=ab⟩ | Infinite non-cancellative commutative monoid | |
| 9 | 2263 | ⟨a, b | ba=ab, aab=aa⟩ | Infinite non-cancellative commutative monoid | 1 iso |
| 9 | 2264 | ⟨a, b | ba=ab, aab=ab⟩ | Infinite non-cancellative commutative monoid | 4 iso |
| 9 | 2266 | ⟨a, b | ba=ab, aab=bb⟩ | Infinite non-cancellative commutative monoid | 1 iso |
| 9 | 2888 | ⟨a, b | aa=a, babab=a⟩ | Infinite non-cancellative commutative monoid | 28 iso |
| 9 | 2968 | ⟨a, b | ab=a, baaaa=a⟩ | Infinite non-cancellative commutative monoid | 23 iso |
| 10 | 4617 | ⟨a, b | aaaa=a, aaba=b⟩ | Infinite non-cancellative commutative monoid | |
| 10 | 4658 | ⟨a, b | aaab=a, abba=b⟩ | Infinite non-cancellative commutative monoid | 1 iso |
| 10 | 4667 | ⟨a, b | aaab=a, babb=a⟩ | Infinite non-cancellative commutative monoid | 3 iso |
| 10 | 5060 | ⟨a, b | aaa=ab, baab=a⟩ | Infinite non-cancellative commutative monoid | 9 iso |
| 10 | 5064 | ⟨a, b | aaa=ab, babb=a⟩ | Infinite non-cancellative commutative monoid | 6 iso |
| 10 | 5287 | ⟨a, b | aba=bb, abbb=b⟩ | Infinite non-cancellative commutative monoid | 13 iso |
| 10 | 5399 | ⟨a, b | aab=ba, bab=ab⟩ | Infinite non-cancellative commutative monoid | 7 iso |
| 10 | 6347 | ⟨a, b | aab=a, abbba=b⟩ | Infinite non-cancellative commutative monoid | 1 iso |
| 10 | 6364 | ⟨a, b | aab=a, babbb=a⟩ | Infinite non-cancellative commutative monoid | 4 iso |
| 10 | 6513 | ⟨a, b | aba=b, abbbb=b⟩ | Infinite non-cancellative commutative monoid | 3 iso |
| 10 | 6762 | ⟨a, b | aba=b, aaaa=aa⟩ | Infinite non-cancellative commutative monoid | |
| 10 | 6982 | ⟨a, b | ab=aa, baaaa=a⟩ | Infinite non-cancellative commutative monoid | 7 iso |
| 10 | 7014 | ⟨a, b | ba=ab, aaaaa=a⟩ | Isomorphic to ℕ(5 = 1) ⊕ ℕ | |
| 10 | 7016 | ⟨a, b | ba=ab, aaaab=a⟩ | Infinite non-cancellative commutative monoid | 2 iso |
| 10 | 7017 | ⟨a, b | ba=ab, aaaab=b⟩ | Infinite non-cancellative commutative monoid | 2 iso |
| 10 | 7020 | ⟨a, b | ba=ab, aaabb=a⟩ | Infinite non-cancellative commutative monoid | 5 iso |
| 10 | 7021 | ⟨a, b | ba=ab, aaabb=b⟩ | Infinite non-cancellative commutative monoid | 5 iso |
| 10 | 7118 | ⟨a, b | ba=ab, aaaa=aa⟩ | Isomorphic to ℕ(4 = 2) ⊕ ℕ | |
| 10 | 7119 | ⟨a, b | ba=ab, aaaa=ab⟩ | Infinite non-cancellative commutative monoid | |
| 10 | 7121 | ⟨a, b | ba=ab, aaab=aa⟩ | Infinite non-cancellative commutative monoid | 1 iso |
| 10 | 7122 | ⟨a, b | ba=ab, aaab=ab⟩ | Infinite non-cancellative commutative monoid | 3 iso |
| 10 | 7124 | ⟨a, b | ba=ab, aaab=bb⟩ | Infinite non-cancellative commutative monoid | 1 iso |
| 10 | 7129 | ⟨a, b | ba=ab, aabb=aa⟩ | Infinite non-cancellative commutative monoid | 3 iso |
| 10 | 7130 | ⟨a, b | ba=ab, aabb=ab⟩ | Infinite non-cancellative commutative monoid | 4 iso |
| 10 | 7186 | ⟨a, b | ba=ab, aab=aaa⟩ | Infinite non-cancellative commutative monoid | 1 iso |
| 10 | 7189 | ⟨a, b | ba=ab, abb=aaa⟩ | Infinite non-cancellative commutative monoid | 1 iso |
| 10 | 7190 | ⟨a, b | ba=ab, abb=aab⟩ | Infinite non-cancellative commutative monoid | 3 iso |
| 10 | 8630 | ⟨a, b | aa=a, babbab=a⟩ | Infinite non-cancellative commutative monoid | 6 iso |
| 10 | 8776 | ⟨a, b | ab=a, baaaaa=a⟩ | Infinite non-cancellative commutative monoid | 6 iso |
| 11 | 12182 | ⟨a, b | aaaa=ab, baab=a⟩ | Infinite non-cancellative commutative monoid | 1 iso |
| 11 | 12186 | ⟨a, b | aaaa=ab, babb=a⟩ | Infinite non-cancellative commutative monoid | |
| 11 | 12288 | ⟨a, b | aaab=ba, babb=a⟩ | Infinite non-cancellative commutative monoid | 5 iso |
| 11 | 12413 | ⟨a, b | aaba=bb, abbb=b⟩ | Infinite non-cancellative commutative monoid | |
| 11 | 12982 | ⟨a, b | abb=aaa, baab=a⟩ | Infinite non-cancellative commutative monoid | 5 iso |
| 11 | 14357 | ⟨a, b | aaaa=a, baaab=a⟩ | Infinite non-cancellative commutative monoid | 5 iso |
| 11 | 14361 | ⟨a, b | aaaa=a, babab=a⟩ | Infinite non-cancellative commutative monoid | |
| 11 | 14455 | ⟨a, b | aaab=a, babbb=a⟩ | Infinite non-cancellative commutative monoid | |
| 11 | 14632 | ⟨a, b | aaba=b, abbbb=b⟩ | Infinite non-cancellative commutative monoid | |
| 11 | 14872 | ⟨a, b | abba=b, bbbbb=b⟩ | Infinite non-cancellative commutative monoid | |
| 11 | 15479 | ⟨a, b | aaa=ab, baabb=a⟩ | Infinite non-cancellative commutative monoid | 2 iso |
| 11 | 15487 | ⟨a, b | aaa=ab, babbb=a⟩ | Infinite non-cancellative commutative monoid | |
| 11 | 15932 | ⟨a, b | aba=bb, abbbb=b⟩ | Infinite non-cancellative commutative monoid | 2 iso |
| 11 | 15944 | ⟨a, b | aba=bb, bbbbb=b⟩ | Infinite non-cancellative commutative monoid | |
| 11 | 16254 | ⟨a, b | aab=ba, babb=ab⟩ | Infinite non-cancellative commutative monoid | 2 iso |
| 11 | 18750 | ⟨a, b | aaa=a, babbab=a⟩ | Infinite non-cancellative commutative monoid | |
| 11 | 18926 | ⟨a, b | aab=a, babbbb=a⟩ | Infinite non-cancellative commutative monoid | 5 iso |
| 11 | 19211 | ⟨a, b | aba=b, abbbbb=b⟩ | Infinite non-cancellative commutative monoid | 3 iso |
| 11 | 19231 | ⟨a, b | aba=b, bbbbbb=b⟩ | Infinite non-cancellative commutative monoid | |
| 11 | 20248 | ⟨a, b | aba=b, aaaa=aaa⟩ | Infinite non-cancellative commutative monoid | |
| 11 | 20584 | ⟨a, b | ab=aa, baaaaa=a⟩ | Infinite non-cancellative commutative monoid | 15 iso |
| 11 | 20648 | ⟨a, b | ba=ab, aaaaaa=a⟩ | Isomorphic to ℕ(6 = 1) ⊕ ℕ | |
| 11 | 20650 | ⟨a, b | ba=ab, aaaaab=a⟩ | Infinite non-cancellative commutative monoid | 2 iso |
| 11 | 20651 | ⟨a, b | ba=ab, aaaaab=b⟩ | Infinite non-cancellative commutative monoid | 2 iso |
| 11 | 20654 | ⟨a, b | ba=ab, aaaabb=a⟩ | Infinite non-cancellative commutative monoid | 8 iso |
| 11 | 20655 | ⟨a, b | ba=ab, aaaabb=b⟩ | Infinite non-cancellative commutative monoid | 8 iso |
| 11 | 20662 | ⟨a, b | ba=ab, aaabbb=a⟩ | Infinite non-cancellative commutative monoid | 9 iso |
| 11 | 20848 | ⟨a, b | ba=ab, aaaaa=aa⟩ | Isomorphic to ℕ(5 = 2) ⊕ ℕ | |
| 11 | 20849 | ⟨a, b | ba=ab, aaaaa=ab⟩ | Infinite non-cancellative commutative monoid | |
| 11 | 20851 | ⟨a, b | ba=ab, aaaab=aa⟩ | Infinite non-cancellative commutative monoid | 2 iso |
| 11 | 20852 | ⟨a, b | ba=ab, aaaab=ab⟩ | Infinite non-cancellative commutative monoid | 4 iso |
| 11 | 20854 | ⟨a, b | ba=ab, aaaab=bb⟩ | Infinite non-cancellative commutative monoid | 2 iso |
| 11 | 20859 | ⟨a, b | ba=ab, aaabb=aa⟩ | Infinite non-cancellative commutative monoid | 5 iso |
| 11 | 20860 | ⟨a, b | ba=ab, aaabb=ab⟩ | Infinite non-cancellative commutative monoid | 9 iso |
| 11 | 20862 | ⟨a, b | ba=ab, aaabb=bb⟩ | Infinite non-cancellative commutative monoid | 5 iso |
| 11 | 21048 | ⟨a, b | ba=ab, aaaa=aaa⟩ | Isomorphic to ℕ(4 = 3) ⊕ ℕ | |
| 11 | 21049 | ⟨a, b | ba=ab, aaaa=aab⟩ | Infinite non-cancellative commutative monoid | 1 iso |
| 11 | 21051 | ⟨a, b | ba=ab, aaaa=abb⟩ | Infinite non-cancellative commutative monoid | 1 iso |
| 11 | 21054 | ⟨a, b | ba=ab, aaab=aaa⟩ | Infinite non-cancellative commutative monoid | 1 iso |
| 11 | 21055 | ⟨a, b | ba=ab, aaab=aab⟩ | Infinite non-cancellative commutative monoid | 5 iso |
| 11 | 21057 | ⟨a, b | ba=ab, aaab=abb⟩ | Infinite non-cancellative commutative monoid | 5 iso |
| 11 | 21061 | ⟨a, b | ba=ab, aaab=bbb⟩ | Infinite non-cancellative commutative monoid | 1 iso |
| 11 | 21070 | ⟨a, b | ba=ab, aabb=aaa⟩ | Infinite non-cancellative commutative monoid | 3 iso |
| 11 | 21071 | ⟨a, b | ba=ab, aabb=aab⟩ | Infinite non-cancellative commutative monoid | 9 iso |
| 11 | 24172 | ⟨a, b | aa=a, babbbab=a⟩ | Infinite non-cancellative commutative monoid | |
| 11 | 24460 | ⟨a, b | ab=a, baaaaaa=a⟩ | Infinite non-cancellative commutative monoid | |