#1531 ⟨a, b | abbaabaaab=1⟩

Properties

Presentation has sum-of-sides 10
Infinite non-Abelian group
Group inverses:
- a^-1 = daca
- b^-1 = ba²da
- c^-1 = a²da
- d^-1 = aca²

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

ca²d ⇒ daca
adac ⇒ daca
daca² ⇒ 1
db ⇒ ba³c
cb ⇒ bc
dab ⇒ abaca²
ca²b ⇒ a²bacdaca
a³b ⇒ ba(ad)²
dacab ⇒ a²baca²c
b² ⇒ c

# ab:abbaabaaab=1 dca/b bb=c,baaab=d frequency:2/3,5/2
caad=daca
adac=daca
dacaa=1
db=baaac
cb=bc
dab=abacaa
caab=aabacdaca
aaab=baadad
dacab=aabacaac
bb=c

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#1531 ⟨a, b | abbaabaaab=1⟩

Properties

Complete rewriting system

Right Cayley graph (truncated)

Left Cayley graph (truncated)