#13151 ⟨a, b | aba=aaa, baa=bb⟩

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:aba=aaa,baa=bb a/b
aaaaaaa=aaaaaa
baaaaa=baaaa
aba=aaa
aaaab=aaaaaa
bb=baa
baab=baaaa

Idempotents are shown in bold.

	1	a	b	a²	ab	ba	a³	a²b	ba²	bab	a⁴	a³b	ba³	a⁵	ba⁴	ba³b	a⁶
1	1	a	b	a²	ab	ba	a³	a²b	ba²	bab	a⁴	a³b	ba³	a⁵	ba⁴	ba³b	a⁶
a	a	a²	ab	a³	a²b	a³	a⁴	a³b	a⁴	a³b	a⁵	a⁶	a⁵	a⁶	a⁶	a⁶	a⁶
b	b	ba	ba²	ba²	bab	ba³	ba³	ba⁴	ba⁴	ba³b	ba⁴	ba³b	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴
a²	a²	a³	a²b	a⁴	a³b	a⁴	a⁵	a⁶	a⁵	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶
ab	ab	a³	a⁴	a⁴	a³b	a⁵	a⁵	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶
ba	ba	ba²	bab	ba³	ba⁴	ba³	ba⁴	ba³b	ba⁴	ba³b	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴
a³	a³	a⁴	a³b	a⁵	a⁶	a⁵	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶
a²b	a²b	a⁴	a⁵	a⁵	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶
ba²	ba²	ba³	ba⁴	ba⁴	ba³b	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴
bab	bab	ba³	ba⁴	ba⁴	ba³b	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴
a⁴	a⁴	a⁵	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶
a³b	a³b	a⁵	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶
ba³	ba³	ba⁴	ba³b	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴
a⁵	a⁵	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶
ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴
ba³b	ba³b	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴	ba⁴
a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶	a⁶

Idempotents are shown in bold.

Idempotents are shown in bold.

16 unique, 71 total

Σ	#	Presentation	Description	Related
10	4375	⟨a, b \| aaaa=b, abbbb=1⟩	Isomorphic to ℤ₁₇	39 iso
10	6428	⟨a, b \| aab=b, babbb=a⟩	Finite non-commutative monoid with 17 elements	2 iso
10	6514	⟨a, b \| aba=b, baaab=a⟩	Finite non-commutative monoid with 17 elements
10	7152	⟨a, b \| bb=aa, abab=aa⟩	Finite non-commutative monoid with 17 elements
10	7153	⟨a, b \| bb=aa, abab=ab⟩	Finite non-commutative monoid with 17 elements
10	7154	⟨a, b \| bb=aa, abab=ba⟩	Finite non-commutative monoid with 17 elements
11	13141	⟨a, b \| aab=aaa, bbb=ab⟩	Finite non-commutative monoid with 17 elements
11	13142	⟨a, b \| aab=aaa, bbb=ba⟩	Finite non-commutative monoid with 17 elements
11	13156	⟨a, b \| aba=aaa, bbb=ab⟩	Finite non-commutative monoid with 17 elements
11	13218	⟨a, b \| abb=aba, bbb=aa⟩	Finite non-commutative monoid with 17 elements
11	14395	⟨a, b \| aaaa=b, abbbb=a⟩	Isomorphic to ℕ_{(17 = 1)}	2 iso
11	14396	⟨a, b \| aaaa=b, abbbb=b⟩	Isomorphic to ℕ_{(17 = 4)}	2 iso
11	14698	⟨a, b \| aabb=a, baaaa=b⟩	Finite non-commutative monoid with 17 elements	1 iso, 6 anti-iso
11	15488	⟨a, b \| aaa=ab, babbb=b⟩	Finite non-commutative monoid with 17 elements	3 iso
11	16143	⟨a, b \| aab=aa, bbbb=ba⟩	Finite non-commutative monoid with 17 elements
11	16521	⟨a, b \| aab=bb, bab=aaa⟩	Finite non-commutative monoid with 17 elements

Up:	Monoids with two generators and two relations
Prev:	#13150 ⟨a, b \| aba=aaa, baa=ba⟩
Next:	#13152 ⟨a, b \| aba=aaa, bab=aa⟩