#21049 ⟨a, b | ba=ab, aaaa=aab⟩

Quick links

Presentation has sum-of-sides 11
Infinite non-cancellative commutative monoid
Not cancellative, because multiplication by a⁶ is not injective:
- a⁶ ⋅ a² = a⁸ and a⁶ ⋅ b = a⁸, however a² ≠ b
Commutative Gröbner basis: ⟨a, b | a²b=a⁴⟩
Cancellative quotient is isomorphic to ℕ
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.	a⁴ ⇒ a²b	[2]

# ab:ba=ab,aaaa=aab ab
ba=ab
aaaa=aab

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

1 total

Σ	#	Presentation	Mapping
11	21050	⟨a, b \| ba=ab, aaaa=aba⟩	φ(a) = a, φ(b) = b

Up:	Monoids with two generators and two relations
Prev:	#21048 ⟨a, b \| ba=ab, aaaa=aaa⟩
Next:	#21051 ⟨a, b \| ba=ab, aaaa=abb⟩