| Up: | Monoid enumeration |
|---|---|
| Prev: | #12 ⟨a, b, c | ab=a, cc=1⟩ |
| Next: | #19 ⟨a, b, c | aa=1, bac=1⟩ |
| # | Rule | Proof |
|---|---|---|
| 1. | (ab)2 ⇒ 1 | [2] |
| 2. | c ⇒ ab | [1] |
# abc:ab=c,cc=1 ab/c - - abab=1 c=ab
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
51 total
| Σ | # | Presentation | Mapping |
|---|---|---|---|
| 5 | 18 | ⟨a, b, c | aa=1, abc=1⟩ | φ(a) = ab, φ(b) = a, φ(c) = b |
| 6 | 123 | ⟨a, b, c | ab=c, abc=1⟩ | φ(a) = a, φ(b) = b, φ(c) = ab |
| 6 | 130 | ⟨a, b, c | ab=c, bca=1⟩ | φ(a) = b, φ(b) = a, φ(c) = ba |
| 6 | 257 | ⟨a, b, c | ab=1, cac=b⟩ | φ(a) = a, φ(b) = bab, φ(c) = b |
| 7 | 265 | ⟨a, b, c | aaa=a, abc=1⟩ | φ(a) = ab, φ(b) = a, φ(c) = b |
| 7 | 301 | ⟨a, b, c | aab=b, abc=1⟩ | φ(a) = ab, φ(b) = a, φ(c) = b |
| 7 | 307 | ⟨a, b, c | aab=b, bca=1⟩ | φ(a) = ab, φ(b) = a, φ(c) = b |
| 7 | 690 | ⟨a, b, c | abc=1, abab=1⟩ | φ(a) = a, φ(b) = b, φ(c) = ab |
| 7 | 751 | ⟨a, b, c | aa=b, acac=1⟩ | φ(a) = a, φ(b) = aa, φ(c) = b |
| 7 | 819 | ⟨a, b, c | ab=a, caca=1⟩ | φ(a) = b, φ(b) = 1, φ(c) = a |
| 7 | 850 | ⟨a, b, c | ab=c, abab=1⟩ | φ(a) = a, φ(b) = b, φ(c) = ab |
| 7 | 866 | ⟨a, b, c | ab=c, baba=1⟩ | φ(a) = b, φ(b) = a, φ(c) = ba |
| 7 | 1065 | ⟨a, b, c | aa=1, aaabc=1⟩ | φ(a) = ab, φ(b) = a, φ(c) = b |
| 7 | 1068 | ⟨a, b, c | aa=1, aabca=1⟩ | φ(a) = ab, φ(b) = a, φ(c) = b |
| 7 | 1071 | ⟨a, b, c | aa=1, abaac=1⟩ | φ(a) = ab, φ(b) = a, φ(c) = b |
| 7 | 1228 | ⟨a, b, c | aa=1, aabc=a⟩ | φ(a) = ab, φ(b) = a, φ(c) = b |
| 7 | 1240 | ⟨a, b, c | aa=1, abca=a⟩ | φ(a) = ab, φ(b) = a, φ(c) = b |
| 7 | 1249 | ⟨a, b, c | aa=1, baac=a⟩ | φ(a) = ab, φ(b) = a, φ(c) = b |
| 7 | 1385 | ⟨a, b, c | aa=1, aaa=bc⟩ | φ(a) = ab, φ(b) = a, φ(c) = b |
| 7 | 1399 | ⟨a, b, c | aa=1, abc=aa⟩ | φ(a) = ab, φ(b) = a, φ(c) = b |
| 8 | 1645 | ⟨a, b, c | aab=ac, bca=1⟩ | φ(a) = b, φ(b) = a, φ(c) = ba |
| 8 | 1832 | ⟨a, b, c | aba=ac, bac=1⟩ | φ(a) = b, φ(b) = a, φ(c) = ab |
| 8 | 1842 | ⟨a, b, c | aba=ac, cba=1⟩ | φ(a) = b, φ(b) = a, φ(c) = ab |
| 8 | 1918 | ⟨a, b, c | abc=aa, bca=1⟩ | φ(a) = ab, φ(b) = a, φ(c) = b |
| 8 | 2324 | ⟨a, b, c | aaa=b, acac=1⟩ | φ(a) = a, φ(b) = aaa, φ(c) = b |
| 8 | 2488 | ⟨a, b, c | aab=c, abab=1⟩ | φ(a) = a, φ(b) = b, φ(c) = aab |
| 8 | 2508 | ⟨a, b, c | aab=c, baba=1⟩ | φ(a) = b, φ(b) = a, φ(c) = bba |
| 8 | 2638 | ⟨a, b, c | aba=c, abab=1⟩ | φ(a) = a, φ(b) = b, φ(c) = aba |
| 8 | 2684 | ⟨a, b, c | abc=a, abab=1⟩ | φ(a) = a, φ(b) = b, φ(c) = aba |
| 8 | 2765 | ⟨a, b, c | abc=b, abab=1⟩ | φ(a) = a, φ(b) = b, φ(c) = abb |
| 8 | 3155 | ⟨a, b, c | ac=ab, baba=1⟩ | φ(a) = b, φ(b) = a, φ(c) = a |
| 8 | 3158 | ⟨a, b, c | ac=ab, baca=1⟩ | φ(a) = b, φ(b) = a, φ(c) = a |
| 8 | 3984 | ⟨a, b, c | abc=1, aaabc=1⟩ | φ(a) = ab, φ(b) = a, φ(c) = b |
| 8 | 3994 | ⟨a, b, c | abc=1, aabca=1⟩ | φ(a) = ab, φ(b) = a, φ(c) = b |
| 8 | 4021 | ⟨a, b, c | abc=1, abcaa=1⟩ | φ(a) = ab, φ(b) = a, φ(c) = b |
| 8 | 4079 | ⟨a, b, c | abc=1, bcaaa=1⟩ | φ(a) = ab, φ(b) = a, φ(c) = b |
| 8 | 4627 | ⟨a, b, c | aa=a, abcbc=1⟩ | φ(a) = 1, φ(b) = a, φ(c) = b |
| 8 | 4652 | ⟨a, b, c | aa=a, bcabc=1⟩ | φ(a) = 1, φ(b) = a, φ(c) = b |
| 8 | 4881 | ⟨a, b, c | ab=a, bcaca=1⟩ | φ(a) = b, φ(b) = 1, φ(c) = a |
| 8 | 4917 | ⟨a, b, c | ab=a, cabca=1⟩ | φ(a) = b, φ(b) = 1, φ(c) = a |
| 8 | 4921 | ⟨a, b, c | ab=a, cacab=1⟩ | φ(a) = b, φ(b) = 1, φ(c) = a |
| 8 | 4923 | ⟨a, b, c | ab=a, cacba=1⟩ | φ(a) = b, φ(b) = 1, φ(c) = a |
| 8 | 4935 | ⟨a, b, c | ab=a, cbaca=1⟩ | φ(a) = b, φ(b) = 1, φ(c) = a |
| 8 | 6884 | ⟨a, b, c | ab=1, abcac=b⟩ | φ(a) = a, φ(b) = bab, φ(c) = b |
| 8 | 6889 | ⟨a, b, c | ab=1, abcbc=a⟩ | φ(a) = aba, φ(b) = b, φ(c) = a |
| 8 | 7079 | ⟨a, b, c | ab=1, caabc=b⟩ | φ(a) = a, φ(b) = bab, φ(c) = b |
| 8 | 7085 | ⟨a, b, c | ab=1, cabac=b⟩ | φ(a) = a, φ(b) = bab, φ(c) = b |
| 8 | 7545 | ⟨a, b, c | ab=1, bcac=bb⟩ | φ(a) = a, φ(b) = bab, φ(c) = b |
| 8 | 7553 | ⟨a, b, c | ab=1, bcbc=ba⟩ | φ(a) = aba, φ(b) = b, φ(c) = a |
| 8 | 7829 | ⟨a, b, c | ab=1, cac=abb⟩ | φ(a) = a, φ(b) = bab, φ(c) = b |
| 8 | 7835 | ⟨a, b, c | ab=1, cac=bab⟩ | φ(a) = a, φ(b) = bab, φ(c) = b |
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
2 total
| Σ | # | Presentation | Mapping |
|---|---|---|---|
| 8 | 3117 | ⟨a, b, c | ab=aa, caca=1⟩ | φ(a) = a, φ(b) = a, φ(c) = b |
| 8 | 3126 | ⟨a, b, c | ab=aa, cbca=1⟩ | φ(a) = a, φ(b) = a, φ(c) = b |