| Up: | Monoid enumeration |
|---|---|
| Prev: | #87 ⟨a, b, c | aa=a, bcb=1⟩ |
| Next: | #92 ⟨a, b, c | aa=b, acc=1⟩ |
| # | Rule | Proof |
|---|---|---|
| 1. | a3c ⇒ 1 | [2] |
| 2. | b ⇒ a2 | [1] |
# abc:aa=b,abc=1 ac/b - - aaac=1 b=aa
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
37 total
| Σ | # | Presentation | Mapping |
|---|---|---|---|
| 6 | 93 | ⟨a, b, c | aa=b, bac=1⟩ | φ(a) = a, φ(b) = aa, φ(c) = c |
| 6 | 121 | ⟨a, b, c | ab=c, aac=1⟩ | φ(a) = a, φ(b) = c, φ(c) = ac |
| 6 | 230 | ⟨a, b, c | ab=1, aac=b⟩ | φ(a) = a, φ(b) = aac, φ(c) = c |
| 6 | 259 | ⟨a, b, c | ab=1, ccc=a⟩ | φ(a) = aaa, φ(b) = c, φ(c) = a |
| 7 | 740 | ⟨a, b, c | aa=b, aaac=1⟩ | φ(a) = a, φ(b) = aa, φ(c) = c |
| 7 | 837 | ⟨a, b, c | ab=a, ccca=1⟩ | φ(a) = c, φ(b) = 1, φ(c) = a |
| 7 | 841 | ⟨a, b, c | ab=c, aaab=1⟩ | φ(a) = a, φ(b) = c, φ(c) = ac |
| 8 | 1677 | ⟨a, b, c | aab=bb, abc=1⟩ | φ(a) = a, φ(b) = aa, φ(c) = c |
| 8 | 1681 | ⟨a, b, c | aab=bb, bac=1⟩ | φ(a) = a, φ(b) = aa, φ(c) = c |
| 8 | 1915 | ⟨a, b, c | abc=aa, bba=1⟩ | φ(a) = ac, φ(b) = a, φ(c) = c |
| 8 | 2313 | ⟨a, b, c | aaa=b, aaac=1⟩ | φ(a) = a, φ(b) = aaa, φ(c) = c |
| 8 | 2479 | ⟨a, b, c | aab=c, aaab=1⟩ | φ(a) = a, φ(b) = c, φ(c) = aac |
| 8 | 2517 | ⟨a, b, c | aab=c, bbba=1⟩ | φ(a) = c, φ(b) = a, φ(c) = cca |
| 8 | 2630 | ⟨a, b, c | aba=c, aaab=1⟩ | φ(a) = a, φ(b) = c, φ(c) = aca |
| 8 | 3164 | ⟨a, b, c | ac=ab, bbba=1⟩ | φ(a) = c, φ(b) = a, φ(c) = a |
| 8 | 3167 | ⟨a, b, c | ac=ab, bbca=1⟩ | φ(a) = c, φ(b) = a, φ(c) = a |
| 8 | 3173 | ⟨a, b, c | ac=ab, bcba=1⟩ | φ(a) = c, φ(b) = a, φ(c) = a |
| 8 | 3176 | ⟨a, b, c | ac=ab, bcca=1⟩ | φ(a) = c, φ(b) = a, φ(c) = a |
| 8 | 4619 | ⟨a, b, c | aa=a, abbbc=1⟩ | φ(a) = 1, φ(b) = a, φ(c) = c |
| 8 | 4899 | ⟨a, b, c | ab=a, bccca=1⟩ | φ(a) = c, φ(b) = 1, φ(c) = a |
| 8 | 4953 | ⟨a, b, c | ab=a, cbcca=1⟩ | φ(a) = c, φ(b) = 1, φ(c) = a |
| 8 | 4971 | ⟨a, b, c | ab=a, ccbca=1⟩ | φ(a) = c, φ(b) = 1, φ(c) = a |
| 8 | 4975 | ⟨a, b, c | ab=a, cccab=1⟩ | φ(a) = c, φ(b) = 1, φ(c) = a |
| 8 | 4977 | ⟨a, b, c | ab=a, cccba=1⟩ | φ(a) = c, φ(b) = 1, φ(c) = a |
| 8 | 6788 | ⟨a, b, c | ab=1, aaabc=b⟩ | φ(a) = a, φ(b) = aac, φ(c) = c |
| 8 | 6802 | ⟨a, b, c | ab=1, aabac=b⟩ | φ(a) = a, φ(b) = aac, φ(c) = c |
| 8 | 6821 | ⟨a, b, c | ab=1, aacab=b⟩ | φ(a) = a, φ(b) = aac, φ(c) = c |
| 8 | 6846 | ⟨a, b, c | ab=1, abaac=b⟩ | φ(a) = a, φ(b) = aac, φ(c) = c |
| 8 | 6898 | ⟨a, b, c | ab=1, abccc=a⟩ | φ(a) = aaa, φ(b) = c, φ(c) = a |
| 8 | 7087 | ⟨a, b, c | ab=1, cabcc=a⟩ | φ(a) = aaa, φ(b) = c, φ(c) = a |
| 8 | 7316 | ⟨a, b, c | ab=1, aaca=ba⟩ | φ(a) = a, φ(b) = aac, φ(c) = c |
| 8 | 7467 | ⟨a, b, c | ab=1, baac=bb⟩ | φ(a) = a, φ(b) = aac, φ(c) = c |
| 8 | 7568 | ⟨a, b, c | ab=1, bccc=ba⟩ | φ(a) = aaa, φ(b) = c, φ(c) = a |
| 8 | 7710 | ⟨a, b, c | ab=1, abb=aac⟩ | φ(a) = a, φ(b) = aac, φ(c) = c |
| 8 | 7741 | ⟨a, b, c | ab=1, bab=aac⟩ | φ(a) = a, φ(b) = aac, φ(c) = c |
| 8 | 7861 | ⟨a, b, c | ab=1, ccc=aab⟩ | φ(a) = aaa, φ(b) = c, φ(c) = a |
| 8 | 7863 | ⟨a, b, c | ab=1, ccc=aba⟩ | φ(a) = aaa, φ(b) = c, φ(c) = a |
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
7 total
| Σ | # | Presentation | Mapping |
|---|---|---|---|
| 8 | 3111 | ⟨a, b, c | ab=aa, caaa=1⟩ | φ(a) = a, φ(b) = a, φ(c) = c |
| 8 | 3112 | ⟨a, b, c | ab=aa, caab=1⟩ | φ(a) = a, φ(b) = a, φ(c) = c |
| 8 | 3114 | ⟨a, b, c | ab=aa, caba=1⟩ | φ(a) = a, φ(b) = a, φ(c) = c |
| 8 | 3115 | ⟨a, b, c | ab=aa, cabb=1⟩ | φ(a) = a, φ(b) = a, φ(c) = c |
| 8 | 3120 | ⟨a, b, c | ab=aa, cbaa=1⟩ | φ(a) = a, φ(b) = a, φ(c) = c |
| 8 | 3121 | ⟨a, b, c | ab=aa, cbab=1⟩ | φ(a) = a, φ(b) = a, φ(c) = c |
| 8 | 3123 | ⟨a, b, c | ab=aa, cbba=1⟩ | φ(a) = a, φ(b) = a, φ(c) = c |