#1533 ⟨a, b | abbaabbaab=1⟩

Quick links

Properties
Rewriting system

Properties

Presentation has sum-of-sides 10
Infinite non-Abelian group
Inverses of generators:
- a^-1 = c²bc²
- b^-1 = acd
- c^-1 = cd
- d^-1 = c²

Rewriting system

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

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

#	Rule	Proof
1.	dc ⇒ cd	[10]
2.	c²d ⇒ 1	[18]
3.	da ⇒ ac³	[21]
4.	c²a ⇒ acd²	[15]
5.	db ⇒ cbc²	[8]
6.	c³b ⇒ bd	[20]
7.	ac²b ⇒ d	[19]
8.	cab ⇒ abc	[7]
9.	cacb ⇒ acbc	[12]
10.	ba ⇒ c	[2]
11.	cbca ⇒ bcac	[11]
12.	abca ⇒ cac	[9]

# ab:abbaabbaab=1 cd/ab ba=c,bcca=d morph:2/0,4/0
dc=cd
ccd=1
da=accc
cca=acdd
db=cbcc
cccb=bd
accb=d
cab=abc
cacb=acbc
ba=c
cbca=bcac
abca=cac