#162 ⟨a, b | ba=ab, bb=b⟩

Properties

Presentation has sum-of-sides 7
Isomorphic to ℕ_{(2 = 1)} ⊕ ℕ
Infinite non-cancellative commutative monoid
Commutative Gröbner basis: ⟨a, b | b²=b⟩
Not cancellative, because multiplication by ab is not injective:
- b ≠ 1
- ab ⋅ b = ab
- ab ⋅ 1 = ab
- Cancellative quotient is isomorphic to ℕ
Grothendieck group is isomorphic to ℤ
Group of units is isomorphic to ℤ₁
4 Archimedian components:
- 1, a, b, ab

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,bb=b ab
ba=ab
bb=b

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

8 total

Σ	#	Presentation	Mapping
8	957	⟨a, b \| aa=a, aab=ba⟩	φ(a) = b, φ(b) = a
9	3005	⟨a, b \| aa=a, aaab=ba⟩	φ(a) = b, φ(b) = a
9	3142	⟨a, b \| aa=a, baa=aab⟩	φ(a) = b, φ(b) = a
10	8845	⟨a, b \| aa=a, aaaab=ba⟩	φ(a) = b, φ(b) = a
10	9122	⟨a, b \| aa=a, aaab=baa⟩	φ(a) = b, φ(b) = a
11	24593	⟨a, b \| aa=a, aaaaab=ba⟩	φ(a) = b, φ(b) = a
11	25126	⟨a, b \| aa=a, aaaab=baa⟩	φ(a) = b, φ(b) = a
11	25686	⟨a, b \| aa=a, baaa=aaab⟩	φ(a) = b, φ(b) = a

Up:	Monoids with two generators and two relations
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Next:	#167 ⟨a, b \| aaa=1, abab=1⟩