| Up: | Monoids with two generators and two relations |
|---|---|
| Prev: | #10846 ⟨a, b | aaba=baa, bbbb=1⟩ |
| Next: | #10872 ⟨a, b | aaba=bba, bbbb=1⟩ |
| order 2 | 1 element | b2 |
| order 4 | 2 elements | b, b3 |
| index 1, period 1 | 1 element | a8 |
| index 1, period 2 | 6561 elements | a4, ba4b3, b2a4b2, a8b2, a7b2a, ... |
| index 1, period 3 | 728 elements | (a4b2)3, (a3b2a)3, (a2b2a2)3, (aba2ba3)2b2, (ab2a3)3, ... |
| index 1, period 4 | 65610 elements | a2, a6, a2b2a2b, ab2a3b, ab2a2ba, ... |
| index 1, period 5 | 26244 elements | ab2a2ba3b2a4b2, b2a2b(a3b2a)2, a2(a3b2a2b)2, a3ba4b2a2ba3b2, a(a2b)2a(a3b2)2, ... |
| index 1, period 6 | 52488 elements | ab2a3b2, b2a3b2a, (a4b)2, (a3ba)2, (a2ba2)2, ... |
| index 1, period 8 | 393660 elements | a, a3, ab3, b3a, a5, ... |
| index 1, period 9 | 58320 elements | a4b2, a3b2a, a2b2a2, ab2a3, ba4b, ... |
| index 1, period 10 | 26244 elements | (a3b)2b, a3b2a3b, a2ba3b2a, (a2b)3, aba3b2a2, ... |
| index 1, period 12 | 524880 elements | a2b2, ab2a, ba2b, b2a2, a4b, ... |
| index 1, period 15 | 209952 elements | a2b3, ab3a, b2a2b, b3a2, (a2b)2, ... |
| index 1, period 24 | 787320 elements | ab, ba, ab2, b2a, a3b, ... |
| index 1, period 30 | 209952 elements | a2b, aba, ba2, ab3a3b, b2(a2b)2, ... |
Rewriting system has 112169 rules, use the Plain view to see.
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baaaaabaaaaaaabaaaaaabaaaaabaaaaaaabaaaaaabaaaaabaaaaaaabaaaab=aaabaaaaaabaabaaaabaaaabaaaaaabaaaaaabaaaaabaaaa baaaaaaabaabaaaabaaaaaaabaaaaaaabbaaaaaabbaaaaab=aaaaaaabaaaabaaaaabaaaabaaaaaabaaaabaaaaaabbaaaaaa baaaabaaaaaabaaaabaaaaaabaabaaaaabaaaabaaaaabaaaaab=abaaaaabaaaaabaaaabaaaaabbaaaaaaabaaaaabbaaa baaaaabaaaaaaabaaaaaabaaaaabaaaaaaabaaaaaabaaaaabaaaaaaabaaaaaab=aaaaaabaaaaabaaaaaabaaaaabaaaabbaaaabaaaaaabaabaa baaaaabaaaaabaaaaaabaaaaaabaaaaaabaaaabbaaaabaaaaba=aaaaaaabaaaaaabaaaaaabaaaabaaaabaaaaaabbaaaaabaaabb
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|---|---|---|
| 11 | 17127 | ⟨a, b | aaaa=1, ababba=b⟩ | φ(a) = bbb, φ(b) = ab |