⟨a, b | abababa=bab⟩

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

#	Rule	Proof
1.	c⁵d ⇒ dc⁵	[15]
2.	bc² ⇒ d	[3]
3.	c⁵b ⇒ dc³	[9]
4.	ac³ ⇒ cb	[5]
5.	c⁴a ⇒ d	[7]
6.	dc⁴d ⇒ c¹¹	[17]
7.	dc⁴b ⇒ c⁹	[16]
8.	dc³a ⇒ c⁶	[11]
9.	bd ⇒ dc²a	[10]
10.	bcd ⇒ c⁶	[8]
11.	bcb ⇒ c⁴	[6]
12.	ba ⇒ c	[2]
13.	ad ⇒ cbca	[12]
14.	acd ⇒ cda	[13]
15.	ac²d ⇒ cdca	[14]

# ab:abababa=bab c/dba ba=c,bcc=d morph:2/0,3/0 cccccd=dccccc bcc=d cccccb=dccc accc=cb cccca=d dccccd=ccccccccccc dccccb=ccccccccc dccca=cccccc bd=dcca bcd=cccccc bcb=cccc ba=c ad=cbca acd=cda accd=cdca

Other submonoids of same group

Σ	#	Presentation	Description	Related
7	131	⟨a, b \| aaaabba=1⟩	Infinite non-Abelian group	11 iso
7	196	⟨a, b \| abbbba=b⟩	Infinite cancellative non-commutative monoid
7	199	⟨a, b \| aaaaa=bb⟩	Infinite cancellative non-commutative monoid
7	232	⟨a, b \| abbba=bb⟩	Infinite cancellative non-commutative monoid
7	237	⟨a, b \| aaaa=bab⟩	Infinite cancellative non-commutative monoid
7	268	⟨a, b \| abba=bbb⟩	Infinite cancellative non-commutative monoid
10	2767	⟨a, b \| babab=ababa⟩	Infinite cancellative non-commutative monoid

Presentation

Description

131

⟨a, b | aaaabba=1⟩

Infinite non-Abelian group

11 iso

196

⟨a, b | abbbba=b⟩

Infinite cancellative non-commutative monoid

199

⟨a, b | aaaaa=bb⟩

Infinite cancellative non-commutative monoid