#1579 ⟨a, b | aaa=aa, aba=b⟩

Properties

Presentation has sum-of-sides 9
Infinite non-cancellative commutative monoid
Commutative Gröbner basis: ⟨a, b | ab=b, a³=a²⟩
Not cancellative, because multiplication by b is not injective:
- a ≠ 1
- b ⋅ a = b
- b ⋅ 1 = b
- Cancellative quotient is isomorphic to ℕ
Grothendieck group is isomorphic to ℤ
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:aaa=aa,aba=b ab
ab=b
ba=b
aaa=aa

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

3 total

Σ	#	Presentation	Mapping
10	5027	⟨a, b \| aaa=aa, aaba=b⟩	φ(a) = a, φ(b) = b
11	15406	⟨a, b \| aaa=aa, aaaba=b⟩	φ(a) = a, φ(b) = b
11	15410	⟨a, b \| aaa=aa, aabaa=b⟩	φ(a) = a, φ(b) = b

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