#4283 ⟨a, b | ababaaaab=aa⟩

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Properties
Rewriting system

Properties

Presentation has sum-of-sides 11
Infinite non-commutative monoid

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

Reduction order:
- Right-to-left recursive path with deg(c) = deg(e) = 0, c < e; deg(d) = deg(a) = 1, d < a; deg(b) = 2
Auxiliary generators:
1. ab=c
2. aaaaa=d
3. cca=e
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	dc ⇒ ec²d	[25]
2.	de ⇒ ec²e²d	[24]
3.	c²a ⇒ e	[4]
4.	da ⇒ ad	[9]
5.	ea²c ⇒ a²	[5]
6.	c²ea²e ⇒ eaca	[12]
7.	c²e²a²e ⇒ ea²	[15]
8.	a³ ⇒ e²a²e	[13]
9.	a²ca ⇒ ea²e	[7]
10.	e³a²ea ⇒ c²d	[19]
11.	aea²e ⇒ e²a²eca	[17]
12.	ae²a²e ⇒ e²a²ea	[18]
13.	eace²a²ec ⇒ c⁴d	[27]
14.	eace²a²e² ⇒ c⁴e²d	[28]
15.	e(ea²)² ⇒ d	[20]
16.	a²cea²e ⇒ ea²eaca	[14]
17.	a²ce²a²e ⇒ (ea²)²	[16]
18.	(e²a²e)² ⇒ ad	[26]
19.	(e²a²ec)² ⇒ ac²d	[29]
20.	e²a²ece²a²e² ⇒ ac²e²d	[30]
21.	eb ⇒ c³	[6]
22.	db ⇒ e²a²eac	[21]
23.	ab ⇒ c	[2]

# ab:ababaaaab=aa reversed:ce/da/b ab=c,aaaaa=d,cca=e morph:2/1,5/0,3/0
dc=eccd
de=ecceed
cca=e
da=ad
eaac=aa
cceaae=eaca
cceeaae=eaa
aaa=eeaae
aaca=eaae
eeeaaea=ccd
aeaae=eeaaeca
aeeaae=eeaaea
eaceeaaec=ccccd
eaceeaaee=cccceed
eeaaeaa=d
aaceaae=eaaeaca
aaceeaae=eaaeaa
eeaaeeeaae=ad
eeaaeceeaaec=accd
eeaaeceeaaee=acceed
eb=ccc
db=eeaaeac
ab=c