#7190 ⟨a, b | ba=ab, abb=aab⟩

Properties

Presentation has sum-of-sides 10
Infinite non-cancellative commutative monoid
Commutative Gröbner basis: ⟨a, b | a²b=ab²⟩
Not cancellative, because multiplication by ab is not injective:
- a ≠ b
- ab ⋅ a = ab²
- ab ⋅ b = ab²
- Cancellative quotient is isomorphic to ℕ
Grothendieck group is isomorphic to ℤ
Group of units is isomorphic to ℤ₁
4 Archimedian components:
- 1, a, b, ab

Format:	Pretty Plain
Word to reduce:
	Tips: Lowercase letters stand for generators. Spaces are ignored. Numbers repeat the previous letter, e.g. `b90`.
Reduction strategy:	Leftmost Rightmost
Path to normal form:	1 1

# ab:ba=ab,abb=aab ab
ba=ab
abb=aab

The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.

3 total

Σ	#	Presentation	Mapping
10	7191	⟨a, b \| ba=ab, abb=aba⟩	φ(a) = a, φ(b) = b
10	7193	⟨a, b \| ba=ab, baa=abb⟩	φ(a) = a, φ(b) = b
10	7195	⟨a, b \| ba=ab, bab=aba⟩	φ(a) = a, φ(b) = b

Up:	Monoids with two generators and two relations
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Next:	#7196 ⟨a, b \| ba=ab, bbb=aaa⟩