#1478 ⟨a, b | abaaaaabba=1⟩

Properties

Presentation has sum-of-sides 10
Infinite non-Abelian group
Group inverses:
- a^-1 = ac
- b^-1 = ba²ba⁵
- c^-1 = a²

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:
- Left-to-right recursive path with deg(a) = deg(c) = 0, a < c; deg(b) = 1
Auxiliary generator: baaaaabb=c

ca ⇒ ac
a²c ⇒ 1
cba²b ⇒ ba⁵bac³
cba⁵b ⇒ ab²a²
a²ba⁵b ⇒ ba²ba⁵
a³b² ⇒ ba⁵bc
b²a²b ⇒ ac³
cba(a²b)² ⇒ ab²a⁷bac³
a(aba²)²b ⇒ ba²ba¹⁰bac³

# ab:abaaaaabba=1 ac/b baaaaabb=c frequency:8/0
ca=ac
aac=1
cbaab=baaaaabaccc
cbaaaaab=abbaa
aabaaaaab=baabaaaaa
aaabb=baaaaabc
bbaab=accc
cbaaabaab=abbaaaaaaabaccc
aabaaabaab=baabaaaaaaaaaabaccc

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#1478 ⟨a, b | abaaaaabba=1⟩

Properties

Complete rewriting system

Right Cayley graph (truncated)

Left Cayley graph (truncated)