#648 ⟨a, b | aaabbbaba=1⟩

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Properties
Rewriting system

Properties

Presentation has sum-of-sides 9
Infinite non-Abelian group
Inverses of generators:
- a^-1 = da³
- b^-1 = b²abc
- c^-1 = d
- d^-1 = c

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(a) = 0, c < d < a; deg(b) = 1
Auxiliary generators:
1. aaaa=c
2. bbbab=d
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	cd ⇒ 1	[10]
2.	dc ⇒ 1	[13]
3.	ac ⇒ ca	[5]
4.	ad ⇒ da	[14]
5.	a⁴ ⇒ c	[2]
6.	abcb ⇒ babc	[23]
7.	a³bab ⇒ (cb)²d	[25]
8.	cb³ ⇒ b²aba³	[19]
9.	db²ab ⇒ b³da	[15]
10.	cab³ ⇒ ab²aba³	[20]
11.	dab²ab ⇒ ab³da	[18]
12.	ca²b³ ⇒ a²b²aba³	[27]
13.	da²b²ab ⇒ a²b³da	[17]
14.	a³b³ ⇒ bcb²da³	[30]
15.	a³b²ab ⇒ cbcb²d	[28]
16.	b³ab ⇒ d	[3]

# ab:aaabbbaba=1 cda/b aaaa=c,bbbab=d magic:0
cd=1
dc=1
ac=ca
ad=da
aaaa=c
abcb=babc
aaabab=cbcbd
cbbb=bbabaaa
dbbab=bbbda
cabbb=abbabaaa
dabbab=abbbda
caabbb=aabbabaaa
daabbab=aabbbda
aaabbb=bcbbdaaa
aaabbab=cbcbbd
bbbab=d