#6513 ⟨a, b | aba=b, abbbb=b⟩

Properties

Presentation has sum-of-sides 10
Infinite non-cancellative commutative monoid
Commutative Gröbner basis: ⟨a, b | a²b=b, b⁴=ab⟩
Not cancellative, because multiplication by ab is not injective:
- a² ≠ 1
- ab ⋅ a² = ab
- ab ⋅ 1 = ab
- 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:aba=b,abbbb=b b/a
bbbbbbb=b
ab=bbbb
ba=bbbb

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

3 total

Σ	#	Presentation	Mapping
10	6521	⟨a, b \| aba=b, babbb=b⟩	φ(a) = a, φ(b) = b
10	6523	⟨a, b \| aba=b, bbabb=b⟩	φ(a) = a, φ(b) = b
10	6796	⟨a, b \| aba=b, bbbb=ab⟩	φ(a) = a, φ(b) = b

Up:	Monoids with two generators and two relations
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Next:	#6514 ⟨a, b \| aba=b, baaab=a⟩