#20851 ⟨a, b | ba=ab, aaaab=aa⟩

Quick links

Presentation has sum-of-sides 11
Infinite non-cancellative commutative monoid
Not cancellative, because multiplication by a²b² is not injective:
- a²b² ⋅ a²b = a²b² and a²b² ⋅ 1 = a²b², however a²b ≠ 1
Commutative Gröbner basis: ⟨a, b | a⁴b=a²⟩
Cancellative quotient is isomorphic to ℤ
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.	a⁴b ⇒ a²	[2]

# ab:ba=ab,aaaab=aa ab
ba=ab
aaaab=aa

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

2 total

Σ	#	Presentation	Mapping
11	20855	⟨a, b \| ba=ab, aaaba=aa⟩	φ(a) = a, φ(b) = b
11	20863	⟨a, b \| ba=ab, aabaa=aa⟩	φ(a) = a, φ(b) = b

Up:	Monoids with two generators and two relations
Prev:	#20850 ⟨a, b \| ba=ab, aaaaa=bb⟩
Next:	#20852 ⟨a, b \| ba=ab, aaaab=ab⟩