#3647 ⟨a, b, c | aaa=1, bbccb=1⟩

Contents

Properties
Rewriting system

Properties

Sum of relation sides is 8
Infinite non-Abelian group
Element aba has infinite order
Inverses of generators:
- a^-1 = a²
- b^-1 = b²c²
- c^-1 = cd
- d^-1 = c²

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

#	Rule	Proof
1.	db ⇒ bd	[4]
2.	dc ⇒ cd	[10]
3.	a³ ⇒ 1	[1]
4.	b³ ⇒ d	[3]
5.	c²b ⇒ bc²	[13]
6.	c²d ⇒ 1	[9]

# abc:aaa=1,bbccb=1 abcd bbb=d morph:3/0
db=bd
dc=cd
aaa=1
bbb=d
ccb=bcc
ccd=1