#4658 ⟨a, b | aaab=a, abba=b⟩

Properties

Presentation has sum-of-sides 10
Infinite non-cancellative commutative monoid
Commutative Gröbner basis: ⟨a, b | a³b=a, a²b²=b⟩
Not cancellative, because multiplication by ab is not injective:
- a²b ≠ 1
- ab ⋅ a²b = ab
- ab ⋅ 1 = ab
Grothendieck group is isomorphic to ℤ
Group of units is isomorphic to ℤ₁
2 Archimedian components:
- 1, 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:aaab=a,abba=b ab
ba=ab
aaab=a
aabb=b

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

1 total

Σ	#	Presentation	Mapping
10	4705	⟨a, b \| aaba=a, abba=b⟩	φ(a) = a, φ(b) = b

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