#1466 ⟨a, b | aabbbbaaab=1⟩

Properties

Presentation has sum-of-sides 10
Infinite non-Abelian group
Group inverses:
- a^-1 = a²ba²b⁴
- 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) = 0; deg(c) = 1; deg(a) = 2
Auxiliary generator: aabbbbaaa=c

cb ⇒ 1
bc ⇒ 1
ba²b⁴a ⇒ aba²b⁴
b³a³ ⇒ a²b⁴ac
ca²b⁴a ⇒ b²a³b
caba² ⇒ a²b⁴ac⁴
ca²ba² ⇒ a²b⁴a²c⁴
a³ba² ⇒ c⁴
ba²b³aba² ⇒ a²ba²b⁸ac⁴
ca²b³aba² ⇒ b²a³bab⁴ac⁴
ba²b²(ba²)² ⇒ a²ba²b⁸a²c⁴
ca²b²(ba²)² ⇒ b²a³bab⁴a²c⁴

# ab:aabbbbaaab=1 b/c/a aabbbbaaa=c frequency:9/4
cb=1
bc=1
baabbbba=abaabbbb
bbbaaa=aabbbbac
caabbbba=bbaaab
cabaa=aabbbbacccc
caabaa=aabbbbaacccc
aaabaa=cccc
baabbbabaa=aabaabbbbbbbbacccc
caabbbabaa=bbaaababbbbacccc
baabbbaabaa=aabaabbbbbbbbaacccc
caabbbaabaa=bbaaababbbbaacccc

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#1466 ⟨a, b | aabbbbaaab=1⟩

Properties

Complete rewriting system

Right Cayley graph (truncated)

Left Cayley graph (truncated)