#21061 ⟨a, b | ba=ab, aaab=bbb⟩

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Presentation has sum-of-sides 11
Infinite non-cancellative commutative monoid
Not cancellative, because multiplication by ab is not injective:
- ab ⋅ a³ = a⁴b and ab ⋅ b² = a⁴b, however a³ ≠ b²
Commutative Gröbner basis: ⟨a, b | b³=a³b⟩
Enveloping 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

#	Rule	Proof
1.	ba ⇒ ab	[1]
2.	a³b ⇒ b³	[2]

# ab:ba=ab,aaab=bbb ab
ba=ab
aaab=bbb

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

1 total

Σ	#	Presentation	Mapping
11	21069	⟨a, b \| ba=ab, aaba=bbb⟩	φ(a) = a, φ(b) = b

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