#16254 ⟨a, b | aab=ba, babb=ab⟩

Properties

Presentation has sum-of-sides 11
Infinite non-cancellative commutative monoid
Commutative Gröbner basis: ⟨a, b | a²b=ab, ab³=ab⟩
Not cancellative, because multiplication by ab is not injective:
- a ≠ 1
- ab ⋅ a = ab
- ab ⋅ 1 = ab
- Cancellative quotient is isomorphic to ℤ₂
Grothendieck group is isomorphic to ℤ₂
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:aab=ba,babb=ab ab
ba=ab
aab=ab
abbb=ab

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

2 total

Σ	#	Presentation	Mapping
11	16266	⟨a, b \| aab=ba, bbba=ab⟩	φ(a) = a, φ(b) = b
11	16403	⟨a, b \| aba=ab, abbb=ba⟩	φ(a) = a, φ(b) = b

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