⟨a, b | abaaab=baaba⟩

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Monoids with two generators and one relation

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

Auxiliary generators:
1. c = baa
2. d = ab
3. e = da
Reduction order:
- Right-to-left recursive path with deg(a) = 0; deg(c) = deg(e) = deg(d) = deg(b) = 1, c < e < d < b
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	ea ⇒ ac	[9]
2.	da ⇒ e	[4]
3.	ab ⇒ d	[3]
4.	ba² ⇒ c	[2]
5.	c²a ⇒ (ac)²	[16]
6.	ace ⇒ c²	[13]
7.	acd ⇒ bae	[10]
8.	cb ⇒ bad	[8]
9.	eb ⇒ d²	[7]
10.	c²e ⇒ bac²	[14]
11.	ece ⇒ dc²	[15]
12.	c²d ⇒ be²	[11]
13.	ecd ⇒ dbae	[12]

# ab:abaaab=baaba reversed:a/cedb baa=c,ab=d,da=e morph:3/2,2/2,2/0 ea=ac da=e ab=d baa=c cca=acac ace=cc acd=bae cb=bad eb=dd cce=bacc ece=dcc ccd=bee ecd=dbae

Other submonoids of same group

Σ	#	Presentation	Description
6	107	⟨a, b \| aabb=ba⟩	Infinite cancellative non-commutative monoid
6	121	⟨a, b \| baa=abb⟩	Infinite cancellative non-commutative monoid
7	217	⟨a, b \| aabab=ba⟩	Infinite cancellative non-commutative monoid
7	262	⟨a, b \| abab=baa⟩	Infinite cancellative non-commutative monoid
8	445	⟨a, b \| aabaab=ba⟩	Infinite cancellative non-commutative monoid
8	541	⟨a, b \| abaab=baa⟩	Infinite cancellative non-commutative monoid
9	927	⟨a, b \| aabaaab=ba⟩	Infinite cancellative non-commutative monoid
9	976	⟨a, b \| abaabab=ba⟩	Infinite cancellative non-commutative monoid
9	1107	⟨a, b \| abaaab=baa⟩	Infinite cancellative non-commutative monoid
9	1249	⟨a, b \| abaab=baba⟩	Infinite cancellative non-commutative monoid
10	1937	⟨a, b \| aabaaaab=ba⟩	Infinite cancellative non-commutative monoid
10	2295	⟨a, b \| abaaaab=baa⟩	Infinite cancellative non-commutative monoid
11	4063	⟨a, b \| aabaaaaab=ba⟩	Infinite cancellative non-commutative monoid
11	4242	⟨a, b \| abaaabaab=ba⟩	Infinite cancellative non-commutative monoid
11	4289	⟨a, b \| ababaabab=ba⟩	Infinite cancellative non-commutative monoid
11	4757	⟨a, b \| abaaaaab=baa⟩	Infinite cancellative non-commutative monoid
11	5349	⟨a, b \| ababaab=baba⟩	Infinite cancellative non-commutative monoid

Presentation

Description

107

⟨a, b | aabb=ba⟩

Infinite cancellative non-commutative monoid

121

⟨a, b | baa=abb⟩

Infinite cancellative non-commutative monoid

217

⟨a, b | aabab=ba⟩

Infinite cancellative non-commutative monoid

262