#1114 ⟨a, b, c | aa=1, bcccb=1⟩

Contents

Properties
Rewriting system

Properties

Sum of relation sides is 7
Infinite non-Abelian group
Element ba has infinite order
Inverses of generators:
- a^-1 = a
- b^-1 = db
- c^-1 = b²c²
- d^-1 = b²

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	[5]
3.	cd ⇒ dc	[7]
4.	db² ⇒ 1	[6]
5.	cb² ⇒ b²c	[10]
6.	c³ ⇒ d	[3]

# abc:aa=1,bcccb=1 adbc ccc=d morph:3/0
aa=1
bd=db
cd=dc
dbb=1
cbb=bbc
ccc=d