#12182 ⟨a, b | aaaa=ab, baab=a⟩

Properties

Presentation has sum-of-sides 11
Infinite non-cancellative commutative monoid
Commutative Gröbner basis: ⟨a, b | a⁸=a, ab=a⁴⟩
Not cancellative, because multiplication by a⁴ is not injective:
- b³ ≠ a²
- a⁴ ⋅ b³ = a⁶
- a⁴ ⋅ a² = a⁶
- Cancellative quotient is isomorphic to ℤ₇
Grothendieck group is isomorphic to ℤ₇
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:aaaa=ab,baab=a a/b
aaaaaaaa=a
ba=aaaa
ab=aaaa

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

1 total

Σ	#	Presentation	Mapping
11	12184	⟨a, b \| aaaa=ab, baba=a⟩	φ(a) = a, φ(b) = b

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