#5356 ⟨a, b | abababa=aaab⟩

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

#	Rule	Proof
1.	cba ⇒ abc	[4]
2.	a³b ⇒ c	[2]
3.	c²a²b ⇒ a²cbc	[10]
4.	abca²b ⇒ cbc	[8]
5.	ca²b²a ⇒ cbc	[7]
6.	ca(ba)² ⇒ a²c	[6]
7.	c(ab)²c ⇒ a²ca²b	[11]
8.	cbca²b ⇒ ca²b²c	[9]
9.	a(ba)³ ⇒ c	[3]
10.	(ab)³c ⇒ ca²b	[5]
11.	c(a²b)² ⇒ aba(bc)²	[12]
12.	ca²b²ca²b ⇒ aba(bc)³	[13]

# ab:abababa=aaab abc aaab=c magic:0
cba=abc
aaab=c
ccaab=aacbc
abcaab=cbc
caabba=cbc
cababa=aac
cababc=aacaab
cbcaab=caabbc
abababa=c
abababc=caab
caabaab=ababcbc
caabbcaab=ababcbcbc