#3181 ⟨a, b | abaaaabbaab=1⟩

Quick links

Properties
Rewriting system

Properties

Presentation has sum-of-sides 11
Infinite non-Abelian group
Inverses of generators:
- a^-1 = bd
- b^-1 = (db)³d²c
- c^-1 = (bd)⁴d
- d^-1 = (bd)³d²bd(db)³d²c

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. abaaaa=c
2. cbba=d
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	b²dbd³bd ⇒ (db)³d²b	[22]
2.	b(bd)³d²bd ⇒ (db)³d³b²	[23]
3.	(db)³d³bd ⇒ b	[20]
4.	b(bd)³dc ⇒ (db)³d³	[21]
5.	(bd)⁴dc ⇒ 1	[17]
6.	cb ⇒ dbd(db)³d²c	[18]
7.	cd ⇒ d(bd²)²(dbd)²(bd³)²c	[26]
8.	a ⇒ (bd)³dc	[16]

# ab:abaaaabbaab=1 reversed:bd/c/a abaaaa=c,cbba=d morph:6/1,4/0
bbdbdddbd=dbdbdbddb
bbdbdbdddbd=dbdbdbdddbb
dbdbdbdddbd=b
bbdbdbddc=dbdbdbddd
bdbdbdbddc=1
cb=dbddbdbdbddc
cd=dbddbdddbddbdbdddbdddc
a=bdbdbddc