⟨a, b | aabbaaaba=b⟩

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

#	Rule	Proof
1.	ca ⇒ ac	[4]
2.	cb²acbc ⇒ ba	[6]
3.	a² ⇒ c	[2]
4.	cb(ba)² ⇒ bab²a(cbc)²	[11]
5.	cb²acba ⇒ b	[5]
6.	(cb²a)² ⇒ bab²acbc	[8]
7.	b³acba ⇒ (cb²ac)²b²	[9]
8.	b³acbc²ba ⇒ cb²ac²b²ab	[12]
9.	bab²acba ⇒ cb²acb²	[7]
10.	bab²acbc²ba ⇒ cb²ab	[10]

# ab:aabbaaaba=b cb/a aa=c morph:2/0 ca=ac cbbacbc=ba aa=c cbbaba=babbacbccbc cbbacba=b cbbacbba=babbacbc bbbacba=cbbaccbbacbb bbbacbccba=cbbaccbbab babbacba=cbbacbb babbacbccba=cbbab

Σ	#	Presentation	Description	Related
10	2558	⟨a, b \| aabbba=babb⟩	Infinite cancellative non-commutative monoid

Presentation

Description

2558

⟨a, b | aabbba=babb⟩

Infinite cancellative non-commutative monoid

Up:	Monoids with two generators and one relation
Prev:	#1711 ⟨a, b \| aabbaaaba=a⟩
Next:	#1713 ⟨a, b \| aabbaaabb=a⟩

#1712 ⟨a, b | aabbaaaba=b⟩

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Properties

Rewriting system

Other submonoids of anti-isomorphic group