#8093 ⟨a, b | aaa=1, bbbb=abb⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 10
- Infinite non-cancellative non-commutative monoid
- Element aba has infinite order
- Not left cancellative, because left multiplication by b is not injective:
-
b ⋅ b7 = b2 and b ⋅ b = b2, however b7 ≠ b
- Not right cancellative, because right multiplication by b is not injective:
-
ab ⋅ b = b4 and b3 ⋅ b = b4, however ab ≠ b3
- 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,bbbb=abb b/a - -
bbbbbbbb=bb
abb=bbbb
aaa=1
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
2 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 22249 | ⟨a, b | aaa=1, aabbbb=bb⟩ | φ(a) = a, φ(b) = b |
| 11 | 22280 | ⟨a, b | aaa=1, abbabb=bb⟩ | φ(a) = a, φ(b) = b |