#4667 ⟨a, b | aaab=a, babb=a⟩

Properties

Presentation has sum-of-sides 10
Infinite non-cancellative commutative monoid
Commutative Gröbner basis: ⟨a, b | a³=ab², ab³=a⟩
Not cancellative, because multiplication by ab is not injective:
- a² ≠ b²
- ab ⋅ a² = a
- ab ⋅ b² = a
- Cancellative quotient is isomorphic to ℤ₆
Grothendieck group is isomorphic to ℤ₆
Group of units is isomorphic to ℤ₁
3 Archimedian components:
- 1, a, b

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:aaab=a,babb=a a/b
aaaaaaa=a
ba=aaaaa
ab=aaaaa

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

3 total

Σ	#	Presentation	Mapping
11	13082	⟨a, b \| bab=aaa, aaab=a⟩	φ(a) = a, φ(b) = b
11	13084	⟨a, b \| bab=aaa, aaba=a⟩	φ(a) = a, φ(b) = b
11	13096	⟨a, b \| bab=aaa, babb=a⟩	φ(a) = a, φ(b) = b

Up:	Monoids with two generators and two relations
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