#10942 ⟨a, b | aabb=bba, bbbb=1⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 11
- Infinite non-cancellative non-commutative monoid
- Element a2ba has infinite order
- Not left cancellative, because left multiplication by a is not injective:
-
a ⋅ a3 = a and a ⋅ 1 = a, however a3 ≠ 1
- Not right cancellative, because right multiplication by a is not injective:
-
a3 ⋅ a = a and 1 ⋅ a = a, however a3 ≠ 1
- Reduction order:
- Left-to-right recursive path with deg(a) = 0; deg(b) = 1
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aabb=bba,bbbb=1 a/b - -
aaaa=a
abb=bbaa
bbbb=1
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
2 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 17111 | ⟨a, b | aaaa=1, aabbaa=b⟩ | φ(a) = b, φ(b) = a |
| 11 | 17633 | ⟨a, b | aaaa=1, aabaa=bb⟩ | φ(a) = b, φ(b) = a |