#14357 ⟨a, b | aaaa=a, baaab=a⟩

Properties

Presentation has sum-of-sides 11
Infinite non-cancellative commutative monoid
Commutative Gröbner basis: ⟨a, b | ab²=a², a⁴=a⟩
Not cancellative, because multiplication by ab is not injective:
- b² ≠ a
- ab ⋅ b² = a²b
- ab ⋅ a = a²b
- Cancellative quotient is isomorphic to ℤ₆
Grothendieck group is isomorphic to ℤ₆
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=a,baaab=a ab
ba=ab
abb=aa
aaaa=a

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

5 total

Σ	#	Presentation	Mapping
11	15766	⟨a, b \| aab=bb, abbba=b⟩	φ(a) = b, φ(b) = a
11	15920	⟨a, b \| aba=bb, aabbb=b⟩	φ(a) = b, φ(b) = a
11	15928	⟨a, b \| aba=bb, abbab=b⟩	φ(a) = b, φ(b) = a
11	15930	⟨a, b \| aba=bb, abbba=b⟩	φ(a) = b, φ(b) = a
11	15936	⟨a, b \| aba=bb, baabb=b⟩	φ(a) = b, φ(b) = a

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