#3285 ⟨a, b | abbabaabaab=1⟩

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Properties
Rewriting system

Properties

Presentation has sum-of-sides 11
Infinite non-Abelian group
Inverses of generators:
- a^-1 = bacdb
- b^-1 = c²d
- c^-1 = cdb
- d^-1 = bc²

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

#	Rule	Proof
1.	dc³ ⇒ c³d	[15]
2.	cb ⇒ d	[3]
3.	bc³ ⇒ c²d	[16]
4.	dc²d ⇒ c	[13]
5.	bc²d ⇒ 1	[12]
6.	dc²a ⇒ cacd	[18]
7.	dac² ⇒ ac²d	[19]
8.	bc²a ⇒ acd	[17]
9.	c²db ⇒ 1	[21]
10.	dbc ⇒ cdb	[24]
11.	abc ⇒ da	[5]
12.	b²c ⇒ db	[23]
13.	dacd ⇒ a	[14]
14.	cdbd ⇒ b	[26]
15.	d²a ⇒ abdc	[8]
16.	daca ⇒ a²cd	[20]
17.	cdba ⇒ bacd	[27]
18.	aba ⇒ c	[2]
19.	d²b ⇒ b²dc	[30]
20.	dcdb ⇒ b²dc²	[31]
21.	dab ⇒ abd	[7]
22.	db² ⇒ b²d	[25]
23.	abda ⇒ dc	[6]
24.	dadbd ⇒ ab²	[28]
25.	d(bd)² ⇒ b³	[29]
26.	dadba ⇒ ab²acd	[32]
27.	(db)²a ⇒ b³acd	[33]

# ab:abbabaabaab=1 reversed:c/dab aba=c,cb=d morph:3/0,2/0
dccc=cccd
cb=d
bccc=ccd
dccd=c
bccd=1
dcca=cacd
dacc=accd
bcca=acd
ccdb=1
dbc=cdb
abc=da
bbc=db
dacd=a
cdbd=b
dda=abdc
daca=aacd
cdba=bacd
aba=c
ddb=bbdc
dcdb=bbdcc
dab=abd
dbb=bbd
abda=dc
dadbd=abb
dbdbd=bbb
dadba=abbacd
dbdba=bbbacd