#1517 ⟨a, b | ababbaaaab=1⟩

Properties

Presentation has sum-of-sides 10
Infinite non-Abelian group
Group inverses:
- a^-1 = e
- b^-1 = a³c³
- c^-1 = eca³c²
- d^-1 = ac³
- e^-1 = a

Complete 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(e) = 0; deg(a) = 1; deg(c) = 2; deg(d) = deg(b) = 3, d < b
Auxiliary generator: ab=c
Auxiliary generator: baa=d
Auxiliary generator: cccd=e

ea ⇒ 1
ae ⇒ 1
ca³ce³ ⇒ acec
ceca ⇒ eca³ce²
c³e ⇒ e⁴ca³c²
ca³c²e³ ⇒ ac²ec
ca³c²a ⇒ a⁴c³
ca³c³ ⇒ a
c³a²ce³ ⇒ e⁴ca³cacec
c³a²c²e³ ⇒ e⁴ca³cac²ec
c³a²c²a ⇒ e⁴ca³ca⁴c³
c³a²c³ ⇒ e⁴ca³ca
d ⇒ eca²
b ⇒ ec

# ab:ababbaaaab=1 reversed:e/a/c/db ab=c,baa=d,cccd=e frequency:2/0,3/2,4/0
ea=1
ae=1
caaaceee=acec
ceca=ecaaacee
ccce=eeeecaaacc
caaacceee=accec
caaacca=aaaaccc
caaaccc=a
cccaaceee=eeeecaaacacec
cccaacceee=eeeecaaacaccec
cccaacca=eeeecaaacaaaaccc
cccaaccc=eeeecaaaca
d=ecaa
b=ec

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#1517 ⟨a, b | ababbaaaab=1⟩

Properties

Complete rewriting system

Right Cayley graph (truncated)

Left Cayley graph (truncated)