#5287 ⟨a, b | abaaaab=abba⟩

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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. abba=c
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	ab²a ⇒ c	[2]
2.	cb²a ⇒ ab²c	[4]
3.	c(ba)² ⇒ ca³c	[8]
4.	aba³c ⇒ cba	[6]
5.	ca⁴b ⇒ cba	[13]
6.	cba³c ⇒ ab²cba	[9]
7.	aba⁴b ⇒ c	[3]
8.	cba⁴b ⇒ ab²c	[7]
9.	cba⁴c ⇒ ca³cba	[10]
10.	ca(a²c)² ⇒ (cb)²a	[12]
11.	cba⁵b ⇒ ca³c	[14]
12.	(ca³)²b ⇒ cbc	[11]

# ab:abaaaab=abba abc abba=c magic:0
abba=c
cbba=abbc
cbaba=caaac
abaaac=cba
caaaab=cba
cbaaac=abbcba
abaaaab=c
cbaaaab=abbc
cbaaaac=caaacba
caaacaac=cbcba
cbaaaaab=caaac
caaacaaab=cbc

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