#317 ⟨a, b | aabbbaba=1⟩

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Properties
Rewriting system

Properties

Presentation has sum-of-sides 8
Infinite non-Abelian group
Inverses of generators:
- a^-1 = da²
- 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. aaa=c
2. bbbab=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.	abcb ⇒ babc	[19]
7.	a(ab)² ⇒ (cb)²d	[21]
8.	cb³ ⇒ b²aba²	[15]
9.	db²ab ⇒ b³da	[12]
10.	cab³ ⇒ ab²aba²	[16]
11.	dab²ab ⇒ ab³da	[14]
12.	a²b³ ⇒ bcb²da²	[26]
13.	a²b²ab ⇒ cbcb²d	[24]
14.	b³ab ⇒ d	[3]

# ab:aabbbaba=1 cda/b aaa=c,bbbab=d magic:0
cd=1
dc=1
ac=ca
ad=da
aaa=c
abcb=babc
aabab=cbcbd
cbbb=bbabaa
dbbab=bbbda
cabbb=abbabaa
dabbab=abbbda
aabbb=bcbbdaa
aabbab=cbcbbd
bbbab=d