#5060 ⟨a, b | aaa=ab, baab=a⟩

Properties

Presentation has sum-of-sides 10
Infinite non-cancellative commutative monoid
Commutative Gröbner basis: ⟨a, b | a⁶=a, ab=a³⟩
Not cancellative, because multiplication by a³ is not injective:
- a² ≠ b
- a³ ⋅ a² = a⁵
- a³ ⋅ b = a⁵
- Cancellative quotient is isomorphic to ℤ₅
Grothendieck group is isomorphic to ℤ₅
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:aaa=ab,baab=a a/b
aaaaaa=a
ba=aaa
ab=aaa

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

9 total

Σ	#	Presentation	Mapping
10	5062	⟨a, b \| aaa=ab, baba=a⟩	φ(a) = a, φ(b) = b
11	12307	⟨a, b \| aaab=bb, abba=b⟩	φ(a) = b, φ(b) = a
11	12409	⟨a, b \| aaba=bb, abab=b⟩	φ(a) = b, φ(b) = a
11	12411	⟨a, b \| aaba=bb, abba=b⟩	φ(a) = b, φ(b) = a
11	14761	⟨a, b \| abab=a, baaaa=a⟩	φ(a) = a, φ(b) = b
11	14860	⟨a, b \| abba=b, abbbb=b⟩	φ(a) = b, φ(b) = a
11	14868	⟨a, b \| abba=b, babbb=b⟩	φ(a) = b, φ(b) = a
11	14870	⟨a, b \| abba=b, bbabb=b⟩	φ(a) = b, φ(b) = a
11	15473	⟨a, b \| aaa=ab, baaaa=a⟩	φ(a) = a, φ(b) = b

Up:	Monoids with two generators and two relations
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Next:	#5064 ⟨a, b \| aaa=ab, babb=a⟩