#3221 ⟨a, b | abaabbbaaba=1⟩

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Properties
Rewriting system

Properties

Presentation has sum-of-sides 11
Infinite non-Abelian group
Inverses of generators:
- a^-1 = acd²
- b^-1 = bd³
- c^-1 = bd⁶
- d^-1 = b²d²

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

#	Rule	Proof
1.	cb ⇒ bc	[5]
2.	b³ ⇒ c	[2]
3.	cdb ⇒ bdc	[22]
4.	db² ⇒ b²d	[14]
5.	dbc ⇒ bcd	[23]
6.	dc² ⇒ c²d	[24]
7.	b²db ⇒ dc	[21]
8.	cd²b ⇒ bd²c	[27]
9.	cd³ ⇒ b	[16]
10.	d³b ⇒ bd³	[26]
11.	d³c ⇒ b	[28]
12.	b²d²b ⇒ d²c	[15]
13.	b²d³ ⇒ 1	[13]
14.	dba ⇒ b²adbd³	[33]
15.	dca ⇒ bcadbd³	[34]
16.	cd²a ⇒ acd²	[20]
17.	d³a ⇒ bd²adbd³	[36]
18.	a² ⇒ dbd³	[17]

# ab:abaabbbaaba=1 bcd/a bbb=c,aab=d morph:3/0,3/0
cb=bc
bbb=c
cdb=bdc
dbb=bbd
dbc=bcd
dcc=ccd
bbdb=dc
cddb=bddc
cddd=b
dddb=bddd
dddc=b
bbddb=ddc
bbddd=1
dba=bbadbddd
dca=bcadbddd
cdda=acdd
ddda=bddadbddd
aa=dbddd