#698 ⟨a, b | abaaaabba=1⟩

Quick links

Properties
Rewriting system

Properties

Presentation has sum-of-sides 9
Infinite non-Abelian group
Inverses of generators:
- a^-1 = dba
- b^-1 = bd²c
- c^-1 = (db)²
- d^-1 = bdbc

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

#	Rule	Proof
1.	b²d² ⇒ (db)²	[23]
2.	dbd² ⇒ b	[21]
3.	b²dbc ⇒ dbd	[22]
4.	(db)²c ⇒ 1	[19]
5.	cb ⇒ bd⁶c	[29]
6.	cd ⇒ d⁴c	[27]
7.	adb ⇒ dba	[6]
8.	ad² ⇒ dbcab	[12]
9.	ab²db ⇒ (db)²abd²	[36]
10.	abd⁴ ⇒ cab³	[33]
11.	ac ⇒ ca	[7]
12.	abdbc ⇒ cab²d	[34]
13.	abd²c ⇒ dbcad	[31]
14.	abd³bc ⇒ cab²	[32]
15.	a² ⇒ dbc	[14]

# ab:abaaaabba=1 reversed:bd/c/a aaaa=c,bcb=d morph:4/0,3/0
bbdd=dbdb
dbdd=b
bbdbc=dbd
dbdbc=1
cb=bddddddc
cd=ddddc
adb=dba
add=dbcab
abbdb=dbdbabdd
abdddd=cabbb
ac=ca
abdbc=cabbd
abddc=dbcad
abdddbc=cabb
aa=dbc