#1241 ⟨a, b | abaab=aaba⟩

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Properties
Rewriting system

Properties

Presentation has sum-of-sides 9
Infinite non-cancellative non-commutative monoid
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ ba²b = a²ba and a ⋅ aba = a²ba, however ba²b ≠ aba
Enveloping group: ⟨a, b | aaabb⟩

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 = abaa
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.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	(cb)² ⇒ c²	[8]
2.	c³b ⇒ cbc²	[11]
3.	cb²cb ⇒ cbc	[9]
4.	cbc²b ⇒ cb²c²	[16]
5.	abcb ⇒ ac	[6]
6.	ac²b ⇒ abc²	[10]
7.	cba ⇒ ac	[12]
8.	c²a ⇒ ac²	[14]
9.	cbca ⇒ cb²ac	[15]
10.	aca ⇒ abac	[13]
11.	caba ⇒ abacb	[5]
12.	cb²a² ⇒ a²bc	[7]
13.	a²ba ⇒ cb	[3]
14.	aba² ⇒ c	[2]

# ab:abaab=aaba bc/a abaa=c morph:4/0
cbcb=cc
cccb=cbcc
cbbcb=cbc
cbccb=cbbcc
abcb=ac
accb=abcc
cba=ac
cca=acc
cbca=cbbac
aca=abac
caba=abacb
cbbaa=aabc
aaba=cb
abaa=c