#671 ⟨a, b | aababbaab=1⟩

Properties

Presentation has sum-of-sides 9
Infinite non-Abelian group
Group inverses:
- a^-1 = adad³
- b^-1 = da²
- c^-1 = d
- d^-1 = c

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(d) = deg(c) = 0, d < c; deg(a) = 1; deg(b) = 2
Auxiliary generator: aab=c
Auxiliary generator: cabb=d

dc ⇒ 1
cd ⇒ 1
dad³a ⇒ adad³
cada ⇒ ad³ac³
cad³a ⇒ da²d
d²a² ⇒ ad³ac
a²da ⇒ c³
(dad)²a ⇒ adad⁶ac³
cad(da)² ⇒ da²d⁴ac³
b ⇒ dad²

# ab:aababbaab=1 dc/a/b aab=c,cabb=d frequency:3/0,4/0
dc=1
cd=1
daddda=adaddd
cada=adddaccc
caddda=daad
ddaa=adddac
aada=ccc
daddada=adaddddddaccc
caddada=daaddddaccc
b=dadd

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#671 ⟨a, b | aababbaab=1⟩

Properties

Complete rewriting system

Right Cayley graph (truncated)

Left Cayley graph (truncated)