#7803 ⟨a, b | aaa=1, abbbb=bb⟩
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:
-
b7 ⋅ b = b2 and b ⋅ b = b2, however b7 ≠ 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,abbbb=bb b/a - -
bbbbbbbb=bb
abb=bbbbbb
aaa=1
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 23324 | ⟨a, b | aaa=1, bbbb=aabb⟩ | φ(a) = a, φ(b) = b |