⟨a, b | abaab=baba⟩

Up:

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

#	Rule	Proof
1.	dc ⇒ cad	[11]
2.	ac² ⇒ ca²d	[12]
3.	dba ⇒ cab	[7]
4.	acba ⇒ ca²b	[9]
5.	aba²d ⇒ cba	[10]
6.	bc ⇒ cab	[13]
7.	bac ⇒ cba	[5]
8.	aba²c ⇒ caba	[8]
9.	aba²b ⇒ c	[2]
10.	b²a ⇒ d	[3]
11.	(ba)² ⇒ c	[4]

# ab:abaab=baba reversed:a/dc/b abaab=c,bba=d morph:5/0,3/0 dc=cad acc=caad dba=cab acba=caab abaad=cba bc=cab bac=cba abaac=caba abaab=c bba=d baba=c

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
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
11	5827	⟨a, b \| abaaab=baaba⟩	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