#1719 ⟨a, b | aabbabaab=a⟩

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Properties
Rewriting system

Properties

Presentation has sum-of-sides 10
Infinite non-cancellative non-commutative monoid
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ ab²aba²b = a and a ⋅ 1 = a, however ab²aba²b ≠ 1
Enveloping group: ⟨a, b | aabaab^-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 = ababa
2. d = ab
Reduction order:
- Right-to-left recursive path with deg(b) = deg(d) = 0, b < d; deg(c) = deg(a) = 1, c < a
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	cb ⇒ d³	[6]
2.	d²cd² ⇒ c	[18]
3.	cd²b ⇒ d	[16]
4.	cdbd² ⇒ d²cdb	[22]
5.	cd³bd² ⇒ cdb	[14]
6.	a ⇒ cd²	[12]
7.	cdbdc ⇒ d⁴cd	[23]
8.	cd³bdc ⇒ d²cd	[24]
9.	c²d² ⇒ d²c²	[20]
10.	cdcd² ⇒ d(dc)²	[17]
11.	cdbcd² ⇒ cd³bc	[25]

# ab:aabbabaab=a reversed:bd/ca ababa=c,ab=d morph:5/0,2/0
cb=ddd
ddcdd=c
cddb=d
cdbdd=ddcdb
cdddbdd=cdb
a=cdd
cdbdc=ddddcd
cdddbdc=ddcd
ccdd=ddcc
cdcdd=ddcdc
cdbcdd=cdddbc