#5904 ⟨a, b | abab=1, aabab=a⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 10
- Infinite non-cancellative non-commutative monoid
- Element a has infinite order
- Not left cancellative, because left multiplication by a is not injective:
-
a ⋅ (ba)2 = a and a ⋅ 1 = a, however (ba)2 ≠ 1
- Not right cancellative, because right multiplication by bab is not injective:
-
(ba)2 ⋅ bab = bab and 1 ⋅ bab = bab, however (ba)2 ≠ 1
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
| # | Rule | Proof |
|---|
| 1. |
(ab)2 ⇒ 1 |
[1] |
# ab:abab=1,aabab=a ab - -
abab=1
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 5912 | ⟨a, b | abab=1, ababa=a⟩ | φ(a) = a, φ(b) = b |