#2339 ⟨a, b | ababbba=baa⟩

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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:
- abab³ ⋅ a = ba² and ba ⋅ a = ba², however abab³ ≠ ba
Enveloping group: ⟨a, b | aaabba^-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 = baa
Reduction order:
- Left-to-right recursive path with deg(b) = deg(c) = 0, b < c; deg(a) = 1
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	abab²c ⇒ ca	[5]
2.	abab³c ⇒ bac	[6]
3.	ba² ⇒ c	[2]
4.	(ba)²c ⇒ cbab³c	[9]
5.	baca ⇒ cbab²c	[7]
6.	cbab³a ⇒ bac	[13]
7.	cbab⁴ac ⇒ bacbab³c	[14]
8.	cbab³ca ⇒ bacbab²c	[12]
9.	c(bab²c)² ⇒ bac²a	[10]
10.	(cbab²)²bc ⇒ (bac)²	[11]
11.	abab³a ⇒ c	[3]
12.	abab⁴ac ⇒ cbab³c	[8]

# ab:ababbba=baa bc/a baa=c magic:0
ababbc=ca
ababbbc=bac
baa=c
babac=cbabbbc
baca=cbabbc
cbabbba=bac
cbabbbbac=bacbabbbc
cbabbbca=bacbabbc
cbabbcbabbc=bacca
cbabbcbabbbc=bacbac
ababbba=c
ababbbbac=cbabbbc