#7188 ⟨a, b | ba=ab, aba=aab⟩
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- Properties
- Staircase diagram
- Rewriting system
- Isomorphic instances
- Presentation has sum-of-sides 10
- Isomorphic to ℕ ⊕ ℕ
- Infinite cancellative commutative monoid
- Commutative Gröbner basis: ⟨a, b | ⟩
- Enveloping group is isomorphic to ℤ ⊕ ℤ
- Group of units is isomorphic to ℤ1
- 4 Archimedian components:
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
| # | Rule | Proof |
|---|
| 1. |
ba ⇒ ab |
[1] |
# ab:ba=ab,aba=aab ab
ba=ab
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 7192 | ⟨a, b | ba=ab, baa=aab⟩ | φ(a) = a, φ(b) = b |