#721 ⟨a, b | abbaaaaab=1⟩

Properties

Presentation has sum-of-sides 9
Infinite non-Abelian group
Group inverses:
- a^-1 = da⁴
- b^-1 = bcba
- 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(c) = deg(d) = deg(a) = 0, c < d < a; deg(b) = 1
Auxiliary generator: aaaaa=c
Auxiliary generator: babb=d

cd ⇒ 1
dc ⇒ 1
ac ⇒ ca
ad ⇒ da
a⁵ ⇒ c
cbab ⇒ bcba
dbcb ⇒ babda⁴
ab² ⇒ bcbda
c(ab)² ⇒ abcba
dabcb ⇒ (ab)²da⁴
ca(ab)² ⇒ a²bcba
da²bcb ⇒ a(ab)²da⁴
ca³bab ⇒ a³bcba
da³bcb ⇒ a³babda⁴
a⁴bcb ⇒ cb²a⁴
a⁴bab ⇒ b²c
b²cb ⇒ da⁴

# ab:abbaaaaab=1 cda/b aaaaa=c,babb=d magic:0
cd=1
dc=1
ac=ca
ad=da
aaaaa=c
cbab=bcba
dbcb=babdaaaa
abb=bcbda
cabab=abcba
dabcb=ababdaaaa
caabab=aabcba
daabcb=aababdaaaa
caaabab=aaabcba
daaabcb=aaababdaaaa
aaaabcb=cbbaaaa
aaaabab=bbc
bbcb=daaaa

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#721 ⟨a, b | abbaaaaab=1⟩

Properties

Complete rewriting system

Right Cayley graph (truncated)

Left Cayley graph (truncated)