#6260 ⟨a, b, c | aa=1, bbcccb=1⟩

Contents

Properties
Rewriting system

Properties

Sum of relation sides is 8
Infinite non-Abelian group
Element ba has infinite order
Inverses of generators:
- a^-1 = a
- b^-1 = db²
- c^-1 = b³c²
- d^-1 = b³

Rewriting system

Format:	Pretty Plain
Word:
	Enter a word above to compute its normal form. Tips: Lowercase letters stand for generators. Spaces are ignored. Numbers repeat the previous letter, e.g. `b90`.
Strategy:	Leftmost Rightmost
Result:	1 1

Auxiliary generators:
1. d = ccc
Reduction order:
- Left-to-right shortlex with a < d < b < c
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	a² ⇒ 1	[1]
2.	bd ⇒ db	[8]
3.	cd ⇒ dc	[5]
4.	c³ ⇒ d	[3]
5.	db³ ⇒ 1	[9]
6.	cb³ ⇒ b³c	[12]

# abc:aa=1,bbcccb=1 adbc ccc=d morph:3/0
aa=1
bd=db
cd=dc
ccc=d
dbbb=1
cbbb=bbbc