#5275 ⟨a, b | aabbbba=baba⟩

Quick links

Properties
Rewriting system

Properties

Presentation has sum-of-sides 11
Infinite non-commutative monoid

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:
- Right-to-left shortlex with b < a < c
Auxiliary generators:
1. baba=c
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	bac ⇒ cba	[4]
2.	(ba)² ⇒ c	[2]
3.	a²b³c ⇒ cba	[6]
4.	cab³c ⇒ babcba	[8]
5.	a²b⁴a ⇒ c	[3]
6.	cab⁴a ⇒ babc	[7]
7.	a²b⁴c ⇒ babc	[10]
8.	(bab)²c ⇒ cab⁴c	[9]
9.	a²b⁵abc ⇒ cab⁴c	[11]
10.	cab⁵abc ⇒ babcab⁴c	[12]

# ab:aabbbba=baba reversed:bac baba=c magic:0
bac=cba
baba=c
aabbbc=cba
cabbbc=babcba
aabbbba=c
cabbbba=babc
aabbbbc=babc
babbabc=cabbbbc
aabbbbbabc=cabbbbc
cabbbbbabc=babcabbbbc

Up:	Monoids with two generators and one relation
Prev:	#5274 ⟨a, b \| aabbbba=baab⟩
Next:	#5276 ⟨a, b \| aabbbba=babb⟩