#15491 ⟨a, b | aaa=ab, bbaab=a⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 11
- Infinite non-cancellative non-commutative monoid
- Element b has infinite order
- Not left cancellative, because left multiplication by a is not injective:
-
a ⋅ b = a3 and a ⋅ a2 = a3, however b ≠ a2
- Not right cancellative, because right multiplication by a is not injective:
-
a7 ⋅ a = a and 1 ⋅ a = a, however a7 ≠ 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:aaa=ab,bbaab=a a/b - -
aaaaaaaa=a
ab=aaa
bba=aaaaa
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 15493 | ⟨a, b | aaa=ab, bbaba=a⟩ | φ(a) = a, φ(b) = b |