#20854 ⟨a, b | ba=ab, aaaab=bb⟩

Properties

Presentation has sum-of-sides 11
Infinite non-cancellative commutative monoid
Commutative Gröbner basis: ⟨a, b | b²=a⁴b⟩
Not cancellative, because multiplication by ab is not injective:
- a⁴ ≠ b
- ab ⋅ a⁴ = a⁵b
- ab ⋅ b = a⁵b
- 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:ba=ab,aaaab=bb ab
ba=ab
aaaab=bb

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

2 total

Σ	#	Presentation	Mapping
11	20858	⟨a, b \| ba=ab, aaaba=bb⟩	φ(a) = a, φ(b) = b
11	20865	⟨a, b \| ba=ab, aabaa=bb⟩	φ(a) = a, φ(b) = b

Up:	Monoids with two generators and two relations
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Next:	#20859 ⟨a, b \| ba=ab, aaabb=aa⟩