⟨a, b | aaababbaba=1⟩

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 = aaaa
2. d = babbab
Reduction order:
- Left-to-right recursive path with deg(a) = deg(c) = 0, a < c; deg(d) = 1; deg(b) = 2
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	ca ⇒ ac	[5]
2.	a⁴ ⇒ c	[2]
3.	dc ⇒ 1	[22]
4.	dac ⇒ a	[18]
5.	da²c ⇒ a²	[19]
6.	da³c ⇒ a³	[21]
7.	ad ⇒ da	[24]
8.	cd ⇒ 1	[23]
9.	cbab ⇒ babc	[31]
10.	dbab ⇒ babd	[25]
11.	d(ab)² ⇒ (ab)²d	[28]
12.	da(ab)² ⇒ a(ab)²d	[29]
13.	da³bab ⇒ a³babd	[30]
14.	ab²ab ⇒ babcbda	[32]
15.	acb²ab ⇒ babc²bda	[33]
16.	a³bab² ⇒ b²aba³	[38]
17.	a³babcb ⇒ cb²aba³	[40]
18.	a³babc²b ⇒ c²b²aba³	[41]
19.	ac²b²ab ⇒ babc³bda	[39]
20.	c³b²ab ⇒ a³babc³bda	[42]
21.	db²ab ⇒ a³ba(bd)²a	[37]
22.	b²abcb ⇒ da³	[36]

# ab:aaababbaba=1 ac/d/b aaaa=c,babbab=d magic:0 ca=ac aaaa=c dc=1 dac=a daac=aa daaac=aaa ad=da cd=1 cbab=babc dbab=babd dabab=ababd daabab=aababd daaabab=aaababd abbab=babcbda acbbab=babccbda aaababb=bbabaaa aaababcb=cbbabaaa aaababccb=ccbbabaaa accbbab=babcccbda cccbbab=aaababcccbda dbbab=aaababdbda bbabcb=daaa

Other submonoids of same group

Σ	#	Presentation	Description
8	388	⟨a, b \| aabbbaa=b⟩	Infinite cancellative non-commutative monoid
8	520	⟨a, b \| aabaa=bbb⟩	Infinite cancellative non-commutative monoid
10	1694	⟨a, b \| aabababaa=b⟩	Infinite cancellative non-commutative monoid
10	2066	⟨a, b \| ababbaba=bb⟩	Infinite cancellative non-commutative monoid
10	2766	⟨a, b \| babab=aabaa⟩	Infinite cancellative non-commutative monoid

Presentation

Description

388

⟨a, b | aabbbaa=b⟩