#3153 ⟨a, b | aabbbbaaaba=1⟩

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Properties
Rewriting system

Properties

Presentation has sum-of-sides 11
Infinite non-Abelian group
Inverses of generators:
- a^-1 = a²cbd
- b^-1 = d²b²
- c^-1 = d²
- d^-1 = cd

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) = deg(b) = 0, c < d < b; deg(a) = 1
Auxiliary generators:
1. bbb=c
2. aaab=d
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	dc ⇒ cd	[9]
2.	bc ⇒ cb	[5]
3.	cd² ⇒ 1	[10]
4.	bd² ⇒ d²b	[14]
5.	b³ ⇒ c	[2]
6.	bda ⇒ d²acbd	[21]
7.	c²da ⇒ b²acbd	[25]
8.	db²a ⇒ cad³b²	[17]
9.	a³ ⇒ d³b²	[15]

# ab:aabbbbaaaba=1 cdb/a bbb=c,aaab=d morph:3/0,4/0
dc=cd
bc=cb
cdd=1
bdd=ddb
bbb=c
bda=ddacbd
ccda=bbacbd
dbba=cadddbb
aaa=dddbb