#19211 ⟨a, b | aba=b, abbbbb=b⟩

Properties

Presentation has sum-of-sides 11
Infinite non-cancellative commutative monoid
Commutative Gröbner basis: ⟨a, b | a²b=b, b⁵=ab⟩
Not cancellative, because multiplication by ab is not injective:
- a² ≠ 1
- ab ⋅ a² = ab
- ab ⋅ 1 = ab
- Cancellative quotient is isomorphic to ℤ₈
Grothendieck group is isomorphic to ℤ₈
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:aba=b,abbbbb=b b/a
bbbbbbbbb=b
ab=bbbbb
ba=bbbbb

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

3 total

Σ	#	Presentation	Mapping
11	19225	⟨a, b \| aba=b, babbbb=b⟩	φ(a) = a, φ(b) = b
11	19229	⟨a, b \| aba=b, bbabbb=b⟩	φ(a) = a, φ(b) = b
11	19774	⟨a, b \| aba=b, bbbbb=ab⟩	φ(a) = a, φ(b) = b

Up:	Monoids with two generators and two relations
Prev:	#19175 ⟨a, b \| aba=b, aaabbb=b⟩
Next:	#19212 ⟨a, b \| aba=b, baaaab=a⟩