#8088 ⟨a, b | aaa=1, babb=bba⟩
Contents
- Properties
- Rewriting system
- Anti-isomorphic instances
- Sum of relation sides is 10
- Infinite non-cancellative non-commutative monoid
- Element ba2 has infinite order
- Not left cancellative, because left multiplication by b is not injective:
-
b ⋅ ba = bab2 and b ⋅ ab2 = bab2, however ba ≠ ab2
- Not right cancellative, because right multiplication by b is not injective:
-
b(ab)3 ⋅ b = b2 and b ⋅ b = b2, however b(ab)3 ≠ b
- Reduction order:
- Left-to-right recursive path with deg(b) = 0; deg(a) = 1
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aaa=1,babb=bba b/a - -
bbbbbbbbbb=bbb
bba=babb
aaa=1
babababb=bb
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 22241 | ⟨a, b | aaa=1, aabbab=bb⟩ | φ(a) = a, φ(b) = b |