#15365 ⟨a, b | aba=bb, aaaaaa=1⟩

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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

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

#	Rule	Proof
1.	eb² ⇒ b	[45]
2.	be ⇒ eb	[46]
3.	e²b ⇒ e	[49]
4.	bceb ⇒ bc	[80]
5.	b³c ⇒ cb³	[38]
6.	ec ⇒ b²ce³	[95]
7.	ebc ⇒ ceb	[77]
8.	deb ⇒ d	[81]
9.	b³d ⇒ db³	[39]
10.	ed ⇒ b²de³	[84]
11.	ebd ⇒ d	[88]
12.	baeb ⇒ ba	[51]
13.	b³a ⇒ ab³	[8]
14.	ea ⇒ b²ae³	[99]
15.	eba ⇒ aeb	[62]
16.	c²b ⇒ b²d	[24]
17.	c²e ⇒ b²de²	[76]
18.	cb²c ⇒ d	[4]
19.	bc² ⇒ db²	[29]
20.	cb²d ⇒ b	[25]
21.	cab ⇒ bae	[40]
22.	cae ⇒ bae³	[97]
23.	bca ⇒ b²ae²	[89]
24.	dc ⇒ cbdb²	[42]
25.	dbc ⇒ bcde³	[96]
26.	db²c ⇒ b	[34]
27.	dbd ⇒ bce²	[98]
28.	db²d ⇒ cb³	[26]
29.	da ⇒ bae	[53]
30.	db²a ⇒ bcbae²	[100]
31.	ac ⇒ ca	[11]
32.	abc ⇒ b²cbae²	[101]
33.	ab²c ⇒ b²dbae²	[92]
34.	ad ⇒ b²ae²	[87]
35.	abd ⇒ b²cb²ae²	[91]
36.	ab²d ⇒ cbae	[55]
37.	a² ⇒ c²	[12]
38.	aba ⇒ b²	[1]
39.	ab²a ⇒ b²cb²	[36]
40.	c³ ⇒ 1	[15]
41.	c²d ⇒ b²c	[17]

# ab:aba=bb,aaaaaa=1 b/e/cda aaaa=c,cbbc=d,dbdbd=e morph:4/0,4/0,5/0
ebb=b
be=eb
eeb=e
bceb=bc
bbbc=cbbb
ec=bbceee
ebc=ceb
deb=d
bbbd=dbbb
ed=bbdeee
ebd=d
baeb=ba
bbba=abbb
ea=bbaeee
eba=aeb
ccb=bbd
cce=bbdee
cbbc=d
bcc=dbb
cbbd=b
cab=bae
cae=baeee
bca=bbaee
dc=cbdbb
dbc=bcdeee
dbbc=b
dbd=bcee
dbbd=cbbb
da=bae
dbba=bcbaee
ac=ca
abc=bbcbaee
abbc=bbdbaee
ad=bbaee
abd=bbcbbaee
abbd=cbae
aa=cc
aba=bb
abba=bbcbb
ccc=1
ccd=bbc