#7130 ⟨a, b | ba=ab, aabb=ab⟩

Properties

Presentation has sum-of-sides 10
Infinite non-cancellative commutative monoid
Commutative Gröbner basis: ⟨a, b | a²b²=ab⟩
Not cancellative, because multiplication by ab is not injective:
- ab ≠ 1
- ab ⋅ ab = ab
- ab ⋅ 1 = ab
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,aabb=ab ab
ba=ab
aabb=ab

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

4 total

Σ	#	Presentation	Mapping
10	7131	⟨a, b \| ba=ab, aabb=ba⟩	φ(a) = a, φ(b) = b
10	7133	⟨a, b \| ba=ab, abab=ab⟩	φ(a) = a, φ(b) = b
10	7134	⟨a, b \| ba=ab, abab=ba⟩	φ(a) = a, φ(b) = b
10	7136	⟨a, b \| ba=ab, abba=ab⟩	φ(a) = a, φ(b) = b

Up:	Monoids with two generators and two relations
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Next:	#7138 ⟨a, b \| bb=aa, aaaa=aa⟩