#339 ⟨a, b | abbbaaab=1⟩

Properties

Presentation has sum-of-sides 8
Infinite non-Abelian group
Group inverses:
- a^-1 = da²
- b^-1 = b²cba
- 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: aaa=c
Auxiliary generator: babbb=d

cd ⇒ 1
dc ⇒ 1
ac ⇒ ca
ad ⇒ da
a³ ⇒ c
cbab ⇒ bcba
dbcb ⇒ babda²
c(ab)² ⇒ abcba
dabcb ⇒ (ab)²da²
ca(ab)² ⇒ a²bcba
da²bcb ⇒ a(ab)²da²
db²cb ⇒ bab²da²
ab³ ⇒ b²cbda
dab²cb ⇒ abab²da²
a²b²cb ⇒ cb³a²
a²bab² ⇒ b³c
b³cb ⇒ da²

# ab:abbbaaab=1 cda/b aaa=c,babbb=d magic:0
cd=1
dc=1
ac=ca
ad=da
aaa=c
cbab=bcba
dbcb=babdaa
cabab=abcba
dabcb=ababdaa
caabab=aabcba
daabcb=aababdaa
dbbcb=babbdaa
abbb=bbcbda
dabbcb=ababbdaa
aabbcb=cbbbaa
aababb=bbbc
bbbcb=daa

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#339 ⟨a, b | abbbaaab=1⟩

Properties

Complete rewriting system

Right Cayley graph (truncated)

Left Cayley graph (truncated)