#4869 ⟨a, b | abbabaab=aba⟩

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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(b) = deg(c) = 0, b < c; deg(d) = deg(a) = 1, d < a
Auxiliary generators:
1. ab=c
2. ccaca=d
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	cdb ⇒ c(bc)²d	[32]
2.	dc ⇒ c²bcd	[31]
3.	ab ⇒ c	[2]
4.	cbcac ⇒ ca	[5]
5.	c³acb ⇒ cac	[13]
6.	c²ac² ⇒ db	[6]
7.	d²b ⇒ d(bc)²d	[34]
8.	(db)² ⇒ db(bc)²d	[33]
9.	cadb ⇒ c³bcd	[35]
10.	cda ⇒ cad	[17]
11.	dac ⇒ c²ac(bc)²d	[37]
12.	dbac ⇒ c²d	[18]
13.	dbcac ⇒ da	[10]
14.	db²cac ⇒ dba	[8]
15.	dbc²acb ⇒ c²d	[28]
16.	ca² ⇒ c³ac	[7]
17.	c(ca)² ⇒ d	[3]
18.	c(ac)² ⇒ cbcd	[16]
19.	(cac)² ⇒ cd	[11]
20.	dadb ⇒ c²bc²(cb)³c³bcd²	[38]
21.	dbadb ⇒ dbc²bcd	[36]
22.	d²a ⇒ dad	[29]
23.	dbda ⇒ dbad	[21]
24.	cada ⇒ c³acd	[20]
25.	da² ⇒ c²acd	[26]
26.	dba² ⇒ dbc²ac	[12]
27.	(da)² ⇒ c²acd²	[22]
28.	dbada ⇒ dbc²acd	[27]

# ab:abbabaab=aba reversed:bc/da ab=c,ccaca=d morph:2/0,5/1
cdb=cbcbcd
dc=ccbcd
ab=c
cbcac=ca
cccacb=cac
ccacc=db
ddb=dbcbcd
dbdb=dbbcbcd
cadb=cccbcd
cda=cad
dac=ccacbcbcd
dbac=ccd
dbcac=da
dbbcac=dba
dbccacb=ccd
caa=cccac
ccaca=d
cacac=cbcd
caccac=cd
dadb=ccbcccbcbcbcccbcdd
dbadb=dbccbcd
dda=dad
dbda=dbad
cada=cccacd
daa=ccacd
dbaa=dbccac
dada=ccacdd
dbada=dbccacd