#3256 ⟨a, b | ababbababba=1⟩

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Properties
Rewriting system

Properties

Presentation has sum-of-sides 11
Infinite non-Abelian group
Inverses of generators:
- a^-1 = c²
- b^-1 = ba²cba
- c^-1 = ac

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

#	Rule	Proof
1.	ca ⇒ ac	[7]
2.	ac² ⇒ 1	[3]
3.	ab² ⇒ ba²cbc	[19]
4.	cb² ⇒ babc³	[6]
5.	cba²cb ⇒ (ab)²c²	[15]
6.	acbab ⇒ b²a²c	[11]
7.	b²a²cb ⇒ c²	[12]
8.	cba(ab)² ⇒ (ab)²c²ba²c	[25]
9.	cba³bab ⇒ a(ba)²cba	[26]
10.	b²a(ab)² ⇒ c²ba²c	[23]
11.	b²a³bab ⇒ acba	[22]

# ab:ababbababba=1 ac/b babba=c morph:5/0
ca=ac
acc=1
abb=baacbc
cbb=babccc
cbaacb=ababcc
acbab=bbaac
bbaacb=cc
cbaabab=ababccbaac
cbaaabab=ababacba
bbaabab=ccbaac
bbaaabab=acba