#1541 ⟨a, b | abbbaaaaab=1⟩

Properties

Presentation has sum-of-sides 10
Infinite non-Abelian group
Group inverses:
- a^-1 = a⁴bab³
- b^-1 = c
- c^-1 = b

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(b) = deg(c) = 0, b < c; deg(a) = 1
Auxiliary generator: abbbaaaaa=c

bc ⇒ 1
cb ⇒ 1
bab³a ⇒ abab³
caba ⇒ ab³ac³
(bab)²a ⇒ abab⁶ac³
ca²ba ⇒ ab³a²c³
bab²a²ba ⇒ abab⁶a²c³
ca³ba ⇒ ab³a³c³
bab²a³ba ⇒ abab⁶a³c³
ca⁴ba ⇒ ab³a⁴c³
cab³a⁴ ⇒ ba⁵b
b²a⁵ ⇒ ab³a⁴c
a⁵ba ⇒ c³
bab²a⁴ba ⇒ abab⁶a⁴c³

# ab:abbbaaaaab=1 bc/a abbbaaaaa=c frequency:9/3
bc=1
cb=1
babbba=ababbb
caba=abbbaccc
babbaba=ababbbbbbaccc
caaba=abbbaaccc
babbaaba=ababbbbbbaaccc
caaaba=abbbaaaccc
babbaaaba=ababbbbbbaaaccc
caaaaba=abbbaaaaccc
cabbbaaaa=baaaaab
bbaaaaa=abbbaaaac
aaaaaba=ccc
babbaaaaba=ababbbbbbaaaaccc

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#1541 ⟨a, b | abbbaaaaab=1⟩

Properties

Complete rewriting system

Right Cayley graph (truncated)

Left Cayley graph (truncated)