#689 ⟨a, b | aabbbabba=1⟩

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Properties
Rewriting system

Properties

Presentation has sum-of-sides 9
Infinite non-Abelian group
Inverses of generators:
- a^-1 = da²
- b^-1 = b²ab²c
- 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. aaa=c
2. bbbabb=d
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	cd ⇒ 1	[9]
2.	dc ⇒ 1	[11]
3.	ac ⇒ ca	[5]
4.	ad ⇒ da	[10]
5.	a³ ⇒ c	[2]
6.	cb³ ⇒ bab²a²	[16]
7.	dbab² ⇒ b³da	[12]
8.	ab²cb ⇒ bab²c	[24]
9.	cab³ ⇒ abab²a²	[17]
10.	dabab² ⇒ ab³da	[15]
11.	a²b³ ⇒ b²cbda²	[26]
12.	a²bab² ⇒ cb²cbd	[23]
13.	db²ab² ⇒ b³abd	[13]
14.	d(ab²)² ⇒ ab³abd	[21]
15.	a(ab²)² ⇒ (cb²)²d	[28]
16.	b³ab² ⇒ d	[3]

# ab:aabbbabba=1 cda/b aaa=c,bbbabb=d magic:0
cd=1
dc=1
ac=ca
ad=da
aaa=c
cbbb=babbaa
dbabb=bbbda
abbcb=babbc
cabbb=ababbaa
dababb=abbbda
aabbb=bbcbdaa
aababb=cbbcbd
dbbabb=bbbabd
dabbabb=abbbabd
aabbabb=cbbcbbd
bbbabb=d