#2984 ⟨a, b | ab=a, bbaaa=a⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 9
- Infinite non-cancellative non-commutative monoid
- Element b has infinite order
- Not left cancellative, because left multiplication by a is not injective:
-
a ⋅ b = a and a ⋅ 1 = a, however b ≠ 1
- Not right cancellative, because right multiplication by a is not injective:
-
a2 ⋅ a = a and 1 ⋅ a = a, however a2 ≠ 1
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:ab=a,bbaaa=a ab - -
ab=a
aaa=a
bba=a
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
16 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 8810 | ⟨a, b | ab=a, bbaaab=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 8812 | ⟨a, b | ab=a, bbaaba=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 8816 | ⟨a, b | ab=a, bbabaa=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 9081 | ⟨a, b | ab=a, bbaaa=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 14457 | ⟨a, b | aaab=a, bbaaa=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 15593 | ⟨a, b | aab=aa, bbaaa=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24530 | ⟨a, b | ab=a, bbaaabb=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24534 | ⟨a, b | ab=a, bbaabab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24536 | ⟨a, b | ab=a, bbaabba=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24542 | ⟨a, b | ab=a, bbabaab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24544 | ⟨a, b | ab=a, bbababa=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24548 | ⟨a, b | ab=a, bbabbaa=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 25057 | ⟨a, b | ab=a, bbaaab=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25061 | ⟨a, b | ab=a, bbaaba=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25069 | ⟨a, b | ab=a, bbabaa=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25599 | ⟨a, b | ab=a, bbaaa=abb⟩ | φ(a) = a, φ(b) = b |