#16313 ⟨a, b | aab=bb, baba=aa⟩

Properties

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:aab=bb,baba=aa a/b
aaaaaaa=aaa
baa=aaaa
aaba=aaaaa
bb=aab
baba=aa

Idempotents are shown in bold.

	1	a	b	a²	ab	ba	a³	a²b	aba	bab	a⁴	a³b	(ab)²	a⁵	a⁴b	a⁶	a⁵b	a⁶b
1	1	a	b	a²	ab	ba	a³	a²b	aba	bab	a⁴	a³b	(ab)²	a⁵	a⁴b	a⁶	a⁵b	a⁶b
a	a	a²	ab	a³	a²b	aba	a⁴	a³b	a⁵	(ab)²	a⁵	a⁴b	a⁵b	a⁶	a⁵b	a³	a⁶b	a³b
b	b	ba	a²b	a⁴	bab	a⁵	a⁵	a⁴b	a²	a⁵b	a⁶	a⁵b	a²b	a³	a⁶b	a⁴	a³b	a⁴b
a²	a²	a³	a²b	a⁴	a³b	a⁵	a⁵	a⁴b	a⁶	a⁵b	a⁶	a⁵b	a⁶b	a³	a⁶b	a⁴	a³b	a⁴b
ab	ab	aba	a³b	a⁵	(ab)²	a⁶	a⁶	a⁵b	a³	a⁶b	a³	a⁶b	a³b	a⁴	a³b	a⁵	a⁴b	a⁵b
ba	ba	a⁴	bab	a⁵	a⁴b	a²	a⁶	a⁵b	a³	a²b	a³	a⁶b	a³b	a⁴	a³b	a⁵	a⁴b	a⁵b
a³	a³	a⁴	a³b	a⁵	a⁴b	a⁶	a⁶	a⁵b	a³	a⁶b	a³	a⁶b	a³b	a⁴	a³b	a⁵	a⁴b	a⁵b
a²b	a²b	a⁵	a⁴b	a⁶	a⁵b	a³	a³	a⁶b	a⁴	a³b	a⁴	a³b	a⁴b	a⁵	a⁴b	a⁶	a⁵b	a⁶b
aba	aba	a⁵	(ab)²	a⁶	a⁵b	a³	a³	a⁶b	a⁴	a³b	a⁴	a³b	a⁴b	a⁵	a⁴b	a⁶	a⁵b	a⁶b
bab	bab	a²	a⁵b	a³	a²b	a⁴	a⁴	a³b	a⁵	a⁴b	a⁵	a⁴b	a⁵b	a⁶	a⁵b	a³	a⁶b	a³b
a⁴	a⁴	a⁵	a⁴b	a⁶	a⁵b	a³	a³	a⁶b	a⁴	a³b	a⁴	a³b	a⁴b	a⁵	a⁴b	a⁶	a⁵b	a⁶b
a³b	a³b	a⁶	a⁵b	a³	a⁶b	a⁴	a⁴	a³b	a⁵	a⁴b	a⁵	a⁴b	a⁵b	a⁶	a⁵b	a³	a⁶b	a³b
(ab)²	(ab)²	a³	a⁶b	a⁴	a³b	a⁵	a⁵	a⁴b	a⁶	a⁵b	a⁶	a⁵b	a⁶b	a³	a⁶b	a⁴	a³b	a⁴b
a⁵	a⁵	a⁶	a⁵b	a³	a⁶b	a⁴	a⁴	a³b	a⁵	a⁴b	a⁵	a⁴b	a⁵b	a⁶	a⁵b	a³	a⁶b	a³b
a⁴b	a⁴b	a³	a⁶b	a⁴	a³b	a⁵	a⁵	a⁴b	a⁶	a⁵b	a⁶	a⁵b	a⁶b	a³	a⁶b	a⁴	a³b	a⁴b
a⁶	a⁶	a³	a⁶b	a⁴	a³b	a⁵	a⁵	a⁴b	a⁶	a⁵b	a⁶	a⁵b	a⁶b	a³	a⁶b	a⁴	a³b	a⁴b
a⁵b	a⁵b	a⁴	a³b	a⁵	a⁴b	a⁶	a⁶	a⁵b	a³	a⁶b	a³	a⁶b	a³b	a⁴	a³b	a⁵	a⁴b	a⁵b
a⁶b	a⁶b	a⁵	a⁴b	a⁶	a⁵b	a³	a³	a⁶b	a⁴	a³b	a⁴	a³b	a⁴b	a⁵	a⁴b	a⁶	a⁵b	a⁶b

Idempotents are shown in bold.

Idempotents are shown in bold.

17 unique, 104 total

Σ	#	Presentation	Description	Related
8	1121	⟨a, b \| aa=1, abbba=b⟩	Finite non-commutative monoid with 18 elements	17 iso
9	3387	⟨a, b \| aa=1, abbbbb=b⟩	Finite non-commutative monoid with 18 elements	22 iso, 9 anti-iso
10	5521	⟨a, b \| aaab=1, bbbbbb=1⟩	Isomorphic to ℤ₁₈	33 iso
10	6732	⟨a, b \| aba=a, aaab=bb⟩	Finite non-commutative monoid with 18 elements
10	6788	⟨a, b \| aba=b, baab=aa⟩	Finite non-commutative monoid with 18 elements
10	6795	⟨a, b \| aba=b, bbbb=aa⟩	Finite non-commutative monoid with 18 elements
10	7039	⟨a, b \| bb=aa, aaaba=b⟩	Finite non-commutative monoid with 18 elements	2 iso
10	8910	⟨a, b \| aa=a, bbbbb=ab⟩	Finite non-commutative monoid with 18 elements	1 iso
11	12187	⟨a, b \| aaaa=ab, babb=b⟩	Finite non-commutative monoid with 18 elements	2 iso
11	15797	⟨a, b \| aab=bb, bbbba=a⟩	Finite non-commutative monoid with 18 elements
11	16042	⟨a, b \| aaa=ab, bbbb=ab⟩	Finite non-commutative monoid with 18 elements
11	16043	⟨a, b \| aaa=ab, bbbb=ba⟩	Finite non-commutative monoid with 18 elements
11	18758	⟨a, b \| aaa=a, bbbbbb=a⟩	Isomorphic to ℕ_{(18 = 6)}
11	18830	⟨a, b \| aaa=b, bbbbbb=a⟩	Isomorphic to ℕ_{(18 = 1)}
11	18831	⟨a, b \| aaa=b, bbbbbb=b⟩	Isomorphic to ℕ_{(18 = 3)}
11	19624	⟨a, b \| aab=b, bbbba=aa⟩	Finite non-commutative monoid with 18 elements
11	20914	⟨a, b \| bb=aa, ababa=aa⟩	Finite non-commutative monoid with 18 elements	1 iso

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