#3387 ⟨a, b | aa=1, abbbbb=b⟩

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:aa=1,abbbbb=b b/a
bbbbbbbbb=b
ab=bbbbb
aa=1

Idempotents are shown in bold.

Idempotents are shown in bold.

Idempotents are shown in bold.

17 unique, 73 total

Σ	#	Presentation	Description	Related
8	1121	⟨a, b \| aa=1, abbba=b⟩	Finite non-commutative monoid with 18 elements	17 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	16313	⟨a, b \| aab=bb, baba=aa⟩	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

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

22 total

Σ	#	Presentation	Mapping
9	3542	⟨a, b \| aa=1, bbbbb=ab⟩	φ(a) = a, φ(b) = b
11	26501	⟨a, b \| aa=1, aaabbbbb=b⟩	φ(a) = a, φ(b) = b
11	26579	⟨a, b \| aa=1, abaabbbb=b⟩	φ(a) = a, φ(b) = b
11	26589	⟨a, b \| aa=1, abababbb=b⟩	φ(a) = a, φ(b) = b
11	26595	⟨a, b \| aa=1, ababbabb=b⟩	φ(a) = a, φ(b) = b
11	26597	⟨a, b \| aa=1, ababbbab=b⟩	φ(a) = a, φ(b) = b
11	26611	⟨a, b \| aa=1, abbaabbb=b⟩	φ(a) = a, φ(b) = b
11	26615	⟨a, b \| aa=1, abbababb=b⟩	φ(a) = a, φ(b) = b
11	26617	⟨a, b \| aa=1, abbabbab=b⟩	φ(a) = a, φ(b) = b
11	26625	⟨a, b \| aa=1, abbbaabb=b⟩	φ(a) = a, φ(b) = b
11	26627	⟨a, b \| aa=1, abbbabab=b⟩	φ(a) = a, φ(b) = b
11	26631	⟨a, b \| aa=1, abbbbaab=b⟩	φ(a) = a, φ(b) = b
11	27081	⟨a, b \| aa=1, aabbbbb=ab⟩	φ(a) = a, φ(b) = b
11	27195	⟨a, b \| aa=1, baabbbb=ab⟩	φ(a) = a, φ(b) = b
11	27206	⟨a, b \| aa=1, bababbb=ab⟩	φ(a) = a, φ(b) = b
11	27210	⟨a, b \| aa=1, babbabb=ab⟩	φ(a) = a, φ(b) = b
11	27214	⟨a, b \| aa=1, babbbab=ab⟩	φ(a) = a, φ(b) = b
11	27224	⟨a, b \| aa=1, bbaabbb=ab⟩	φ(a) = a, φ(b) = b
11	27228	⟨a, b \| aa=1, bbababb=ab⟩	φ(a) = a, φ(b) = b
11	27689	⟨a, b \| aa=1, abbbbb=aab⟩	φ(a) = a, φ(b) = b
11	27692	⟨a, b \| aa=1, abbbbb=baa⟩	φ(a) = a, φ(b) = b
11	28287	⟨a, b \| aa=1, bbbbb=aaab⟩	φ(a) = a, φ(b) = b

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

9 total

Σ	#	Presentation	Mapping
11	26553	⟨a, b \| aa=1, aabbbbba=b⟩	φ(a) = a, φ(b) = b
11	27082	⟨a, b \| aa=1, aabbbbb=ba⟩	φ(a) = a, φ(b) = b
11	27162	⟨a, b \| aa=1, abbbbba=ab⟩	φ(a) = a, φ(b) = b
11	27196	⟨a, b \| aa=1, baabbbb=ba⟩	φ(a) = a, φ(b) = b
11	27207	⟨a, b \| aa=1, bababbb=ba⟩	φ(a) = a, φ(b) = b
11	27211	⟨a, b \| aa=1, babbabb=ba⟩	φ(a) = a, φ(b) = b
11	27225	⟨a, b \| aa=1, bbaabbb=ba⟩	φ(a) = a, φ(b) = b
11	27690	⟨a, b \| aa=1, abbbbb=aba⟩	φ(a) = a, φ(b) = b
11	28288	⟨a, b \| aa=1, bbbbb=aaba⟩	φ(a) = a, φ(b) = b

Up:	Monoids with two generators and two relations
Prev:	#3385 ⟨a, b \| aa=1, abbbba=b⟩
Next:	#3397 ⟨a, b \| aa=1, bababb=b⟩