#660 ⟨a, b | aabaababa=1⟩

Properties

Presentation has sum-of-sides 9
Infinite non-Abelian group
Group inverses:
- a^-1 = bacd
- b^-1 = a²c²
- c^-1 = cd
- d^-1 = c²

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(c) = deg(d) = 0, c < d; deg(b) = deg(a) = 1, b < a
Auxiliary generator: aba=c
Auxiliary generator: baa=d

dc ⇒ cd
c²d ⇒ 1
c²b ⇒ dbc
d²b ⇒ bcd
ca ⇒ ad
da ⇒ ac⁴
dba ⇒ bac
ab ⇒ cbacd
adb ⇒ bad
bacb ⇒ dbcbacd
bacdb ⇒ db²ad
ba² ⇒ d

# ab:aabaababa=1 cd/ba aba=c,baa=d frequency:3/0,3/4
dc=cd
ccd=1
ccb=dbc
ddb=bcd
ca=ad
da=acccc
dba=bac
ab=cbacd
adb=bad
bacb=dbcbacd
bacdb=dbbad
baa=d

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#660 ⟨a, b | aabaababa=1⟩

Properties

Complete rewriting system

Right Cayley graph (truncated)

Left Cayley graph (truncated)