#19725 ⟨a, b | aba=b, aabab=bb⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 11
- Infinite non-cancellative non-commutative monoid
- Element a has infinite order
- Not left cancellative, because left multiplication by b is not injective:
-
b ⋅ ba = b2 and b ⋅ b = b2, however ba ≠ b
- Not right cancellative, because right multiplication by b is not injective:
-
ab ⋅ b = b2 and b ⋅ b = b2, however ab ≠ b
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aba=b,aabab=bb ab - -
aba=b
abb=bb
bba=bb
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
3 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 19740 | ⟨a, b | aba=b, ababa=bb⟩ | φ(a) = a, φ(b) = b |
| 11 | 20281 | ⟨a, b | aba=b, abab=abb⟩ | φ(a) = a, φ(b) = b |
| 11 | 20284 | ⟨a, b | aba=b, abab=bba⟩ | φ(a) = a, φ(b) = b |