#5328 ⟨a, b | abaabba=abab⟩

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

#	Rule	Proof
1.	cab ⇒ abc	[4]
2.	(ab)² ⇒ c	[2]
3.	ca²b²a ⇒ abc	[7]
4.	ca²b²c ⇒ abcbab	[8]
5.	aba²b²a ⇒ c	[3]
6.	aba²b²c ⇒ cbab	[6]
7.	cba²b²a ⇒ cbab	[10]
8.	c(bab)² ⇒ cba²b²c	[9]
9.	cb(ab²a)² ⇒ cba²b²c	[11]
10.	cbab²a²b²c ⇒ cba²b²cbab	[12]

# ab:abaabba=abab abc abab=c magic:0
cab=abc
abab=c
caabba=abc
caabbc=abcbab
abaabba=c
abaabbc=cbab
cbaabba=cbab
cbabbab=cbaabbc
cbabbaabba=cbaabbc
cbabbaabbc=cbaabbcbab

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