#5241 ⟨a, b | aabbbaa=aaba⟩

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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 b < a < c
Auxiliary generators:
1. aaba=c
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	a²ba ⇒ c	[2]
2.	caba ⇒ a²bc	[4]
3.	c(ba)² ⇒ cb³c	[10]
4.	a²b³c ⇒ cba	[7]
5.	cb³a² ⇒ cba	[15]
6.	cb³ac ⇒ cbc	[14]
7.	cab³c ⇒ a²bcba	[11]
8.	a²b³a² ⇒ c	[3]
9.	a²b³ac ⇒ a²bc	[8]
10.	cbab³c ⇒ cb³cba	[12]
11.	cab³a² ⇒ a²bc	[17]
12.	cab³ac ⇒ cabc	[9]
13.	cbab³a² ⇒ cb³c	[16]
14.	cbab³ac ⇒ cbabc	[13]

# ab:aabbbaa=aaba bac aaba=c magic:0
aaba=c
caba=aabc
cbaba=cbbbc
aabbbc=cba
cbbbaa=cba
cbbbac=cbc
cabbbc=aabcba
aabbbaa=c
aabbbac=aabc
cbabbbc=cbbbcba
cabbbaa=aabc
cabbbac=cabc
cbabbbaa=cbbbc
cbabbbac=cbabc