#2611 ⟨a, b | ababba=bbaa⟩

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Properties
Rewriting system

Properties

Presentation has sum-of-sides 10
Infinite non-cancellative non-commutative monoid
Not right cancellative, because right multiplication by a is not injective:
- abab² ⋅ a = b²a² and b²a ⋅ a = b²a², however abab² ≠ b²a
Enveloping group: ⟨a, b | aabba^-1a^-1b^-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 = bbaa
Reduction order:
- Left-to-right shortlex with a < b < c
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	abac ⇒ ca	[5]
2.	b²a² ⇒ c	[2]
3.	b²aca ⇒ cbac	[7]
4.	abab²a ⇒ c	[3]
5.	abab²c ⇒ b²ac	[6]
6.	cbab²a ⇒ b²ac	[12]
7.	(b²a)²c ⇒ cbab²c	[10]
8.	cbab²ca ⇒ b(bac)²	[13]
9.	c(bac)² ⇒ b²ac²a	[8]
10.	abab⁴ac ⇒ cbab²c	[9]
11.	cbab⁴ac ⇒ b²acbab²c	[14]
12.	(cba)²b²c ⇒ (b²ac)²	[11]

# ab:ababba=bbaa abc bbaa=c magic:0
abac=ca
bbaa=c
bbaca=cbac
ababba=c
ababbc=bbac
cbabba=bbac
bbabbac=cbabbc
cbabbca=bbacbac
cbacbac=bbacca
ababbbbac=cbabbc
cbabbbbac=bbacbabbc
cbacbabbc=bbacbbac