#2756 ⟨a, b | baabb=aabba⟩

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Properties
Rewriting system

Properties

Presentation has sum-of-sides 10
Infinite cancellative non-commutative monoid
Submonoid of enveloping group: ⟨a, b | aabbab^-1b^-1a^-1a^-1b^-1⟩

Anti-isomorphic embedding: φ(a) = a^-1, φ(b) = b^-1

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

Auxiliary generators:
1. c = aab
Reduction order:
- Left-to-right shortlex with b < a < c
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	a²b ⇒ c	[2]
2.	cba ⇒ bcb	[4]
3.	b²cb² ⇒ cbc	[5]
4.	cbcb² ⇒ a²cbc	[6]
5.	cbc²b² ⇒ b²c²bc	[7]

# ab:baabb=aabba bac aab=c morph:3/1
aab=c
cba=bcb
bbcbb=cbc
cbcbb=aacbc
cbccbb=bbccbc