#20651 ⟨a, b | ba=ab, aaaaab=b⟩

Properties

Presentation has sum-of-sides 11
Infinite non-cancellative commutative monoid
Commutative Gröbner basis: ⟨a, b | a⁵b=b⟩
Not cancellative, because multiplication by ab is not injective:
- a⁵ ≠ 1
- ab ⋅ a⁵ = ab
- ab ⋅ 1 = ab
- Cancellative quotient is isomorphic to ℤ₅ ⊕ ℕ
Grothendieck group is isomorphic to ℤ₅ ⊕ 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,aaaaab=b ab
ba=ab
aaaaab=b

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

2 total

Σ	#	Presentation	Mapping
11	20653	⟨a, b \| ba=ab, aaaaba=b⟩	φ(a) = a, φ(b) = b
11	20657	⟨a, b \| ba=ab, aaabaa=b⟩	φ(a) = a, φ(b) = b

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