| Up: | Monoid enumeration |
|---|---|
| Prev: | #1585 ⟨a, b | aaa=aa, bbb=b⟩ |
| Next: | #1590 ⟨a, b | aaa=ab, abb=a⟩ |
| # | Rule | Proof |
|---|---|---|
| 1. | a4 ⇒ a | [2] |
| 2. | ab ⇒ a3 | [1] |
# ab:aaa=ab,aab=a a/b - - aaaa=a ab=aaa
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
45 total
| Σ | # | Presentation | Mapping |
|---|---|---|---|
| 9 | 1588 | ⟨a, b | aaa=ab, aba=a⟩ | φ(a) = a, φ(b) = b |
| 9 | 2020 | ⟨a, b | aab=a, aaaa=a⟩ | φ(a) = a, φ(b) = b |
| 9 | 2034 | ⟨a, b | aab=a, abbb=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 5042 | ⟨a, b | aaa=ab, aaaa=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 12459 | ⟨a, b | aabb=ab, abbb=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 12568 | ⟨a, b | abba=ab, abbb=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 18834 | ⟨a, b | aab=a, aaaaab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 18836 | ⟨a, b | aab=a, aaaaba=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 18840 | ⟨a, b | aab=a, aaabaa=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 18848 | ⟨a, b | aab=a, aabaaa=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 18862 | ⟨a, b | aab=a, aabbbb=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 18864 | ⟨a, b | aab=a, abaaaa=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 18878 | ⟨a, b | aab=a, ababbb=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 18886 | ⟨a, b | aab=a, abbabb=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 18890 | ⟨a, b | aab=a, abbbab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 18892 | ⟨a, b | aab=a, abbbba=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 19090 | ⟨a, b | aba=a, aaaaab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 19134 | ⟨a, b | aba=a, abbbab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 19376 | ⟨a, b | aab=a, aaaaa=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 19381 | ⟨a, b | aab=a, aaaab=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 19385 | ⟨a, b | aab=a, aaaba=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 19393 | ⟨a, b | aab=a, aabaa=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 19404 | ⟨a, b | aab=a, aabbb=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 19409 | ⟨a, b | aab=a, abaaa=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 19420 | ⟨a, b | aab=a, ababb=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 19428 | ⟨a, b | aab=a, abbab=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 19432 | ⟨a, b | aab=a, abbba=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 19437 | ⟨a, b | aab=a, abbbb=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 19442 | ⟨a, b | aab=a, baaaa=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 19470 | ⟨a, b | aab=a, babbb=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 19640 | ⟨a, b | aba=a, aaaba=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 19648 | ⟨a, b | aba=a, aabaa=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 19921 | ⟨a, b | aab=a, aaaa=aab⟩ | φ(a) = a, φ(b) = b |
| 11 | 19922 | ⟨a, b | aab=a, aaaa=aba⟩ | φ(a) = a, φ(b) = b |
| 11 | 19931 | ⟨a, b | aab=a, aaab=abb⟩ | φ(a) = a, φ(b) = b |
| 11 | 19939 | ⟨a, b | aab=a, aaba=abb⟩ | φ(a) = a, φ(b) = b |
| 11 | 19944 | ⟨a, b | aab=a, aabb=aaa⟩ | φ(a) = a, φ(b) = b |
| 11 | 19955 | ⟨a, b | aab=a, abaa=abb⟩ | φ(a) = a, φ(b) = b |
| 11 | 19960 | ⟨a, b | aab=a, abab=aaa⟩ | φ(a) = a, φ(b) = b |
| 11 | 19968 | ⟨a, b | aab=a, abba=aaa⟩ | φ(a) = a, φ(b) = b |
| 11 | 19977 | ⟨a, b | aab=a, abbb=aab⟩ | φ(a) = a, φ(b) = b |
| 11 | 19978 | ⟨a, b | aab=a, abbb=aba⟩ | φ(a) = a, φ(b) = b |
| 11 | 19989 | ⟨a, b | aab=a, baaa=bab⟩ | φ(a) = a, φ(b) = b |
| 11 | 20012 | ⟨a, b | aab=a, babb=baa⟩ | φ(a) = a, φ(b) = b |
| 11 | 20206 | ⟨a, b | aba=a, abab=aaa⟩ | φ(a) = a, φ(b) = b |
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
5 total
| Σ | # | Presentation | Mapping |
|---|---|---|---|
| 9 | 1649 | ⟨a, b | aab=bb, abb=b⟩ | φ(a) = b, φ(b) = a |
| 10 | 5193 | ⟨a, b | aab=bb, aaab=b⟩ | φ(a) = b, φ(b) = a |
| 11 | 12613 | ⟨a, b | abbb=bb, bbbb=b⟩ | φ(a) = b, φ(b) = a |
| 11 | 19641 | ⟨a, b | aba=a, aaaba=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 20187 | ⟨a, b | aba=a, aaab=bab⟩ | φ(a) = a, φ(b) = b |