#17663 ⟨a, b | aaaa=1, abbba=bb⟩

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

#	Rule	Proof
1.	db³ ⇒ b²	[95]
2.	bd ⇒ db	[126]
3.	d²b ⇒ d	[128]
4.	bcdb ⇒ bc	[89]
5.	b⁵c ⇒ cb⁵	[72]
6.	dc ⇒ b⁴cd⁵	[151]
7.	dbc ⇒ cdb	[141]
8.	db²c ⇒ bc	[111]
9.	cb³c ⇒ b²	[71]
10.	bc²db ⇒ bc²	[90]
11.	b²c² ⇒ cbcb³	[76]
12.	b³cbc ⇒ c²b²	[49]
13.	c³b² ⇒ b³c	[63]
14.	c³d ⇒ b³cd³	[115]
15.	c(bc)² ⇒ b²cd³	[112]
16.	bc³ ⇒ b⁴cd²	[106]
17.	c³bc ⇒ b³cb⁴cd⁵	[153]
18.	ab² ⇒ b²c	[15]
19.	ad ⇒ b²cd³	[129]
20.	acb² ⇒ db²	[124]
21.	acd ⇒ d²	[134]
22.	abc ⇒ b²cb⁴cd⁵	[152]
23.	ac²b² ⇒ b⁴cd³	[150]
24.	ac²d ⇒ b⁴cd⁶	[154]
25.	acbc ⇒ cdb	[140]
26.	ac²bc ⇒ bc²d³	[144]
27.	b²a ⇒ b⁴cd²	[120]
28.	da ⇒ bcd²	[149]
29.	dba ⇒ b²cd²	[121]
30.	cba ⇒ bac	[10]
31.	bca ⇒ bcb²cd²	[147]
32.	bc²a ⇒ bc²b²cd²	[148]
33.	(ba)³ ⇒ c	[3]
34.	ca³ ⇒ b(ab)²	[8]
35.	a⁴ ⇒ 1	[1]

# ab:aaaa=1,abbba=bb b/d/c/a bababa=c,cbcbcbc=d morph:6/0,7/0
dbbb=bb
bd=db
ddb=d
bcdb=bc
bbbbbc=cbbbbb
dc=bbbbcddddd
dbc=cdb
dbbc=bc
cbbbc=bb
bccdb=bcc
bbcc=cbcbbb
bbbcbc=ccbb
cccbb=bbbc
cccd=bbbcddd
cbcbc=bbcddd
bccc=bbbbcdd
cccbc=bbbcbbbbcddddd
abb=bbc
ad=bbcddd
acbb=dbb
acd=dd
abc=bbcbbbbcddddd
accbb=bbbbcddd
accd=bbbbcdddddd
acbc=cdb
accbc=bccddd
bba=bbbbcdd
da=bcdd
dba=bbcdd
cba=bac
bca=bcbbcdd
bcca=bccbbcdd
bababa=c
caaa=babab
aaaa=1