#5192 ⟨a, b | aababba=aaab⟩

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

#	Rule	Proof
1.	a³b ⇒ c	[2]
2.	cab²a ⇒ ac	[6]
3.	cab²c ⇒ aca²b	[7]
4.	a²bab²a ⇒ c	[3]
5.	a²bab²c ⇒ ca²b	[5]
6.	cabab²a ⇒ ca²b	[9]
7.	c(a²b)² ⇒ cabab²c	[8]
8.	ca(ab)³ba ⇒ cabab²c	[10]
9.	ca(ab)³bc ⇒ cabab²ca²b	[11]

# ab:aababba=aaab bac aaab=c magic:0
aaab=c
cabba=ac
cabbc=acaab
aababba=c
aababbc=caab
cababba=caab
caabaab=cababbc
caabababba=cababbc
caabababbc=cababbcaab

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