#686 ⟨a, b | aabbbaaab=1⟩

Properties

Presentation has sum-of-sides 9
Infinite non-Abelian group
Group inverses:
- a^-1 = ba²ca²
- b^-1 = b²d
- 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:
- Right-to-left recursive path with deg(c) = deg(d) = deg(b) = 0, c < d < b; deg(a) = 1
Auxiliary generator: bbb=c
Auxiliary generator: aaabaa=d

dc ⇒ 1
cd ⇒ 1
cb ⇒ bc
db ⇒ bd
b³ ⇒ c
aba²c ⇒ ba²ca
a²cad ⇒ b²daba²
a³b ⇒ bda²ca
aba²bc ⇒ ba²cab
a²cabd ⇒ b²daba²b
aba²b² ⇒ ca³
a²cab² ⇒ b²a³c
a²ca²d ⇒ b²da²ba²
a²ca²bd ⇒ b²d(a²b)²
a²ca²b² ⇒ b²daca³c
a²ca³ ⇒ b²d

# ab:aabbbaaab=1 reversed:cdb/a bbb=c,aaabaa=d magic:1
dc=1
cd=1
cb=bc
db=bd
bbb=c
abaac=baaca
aacad=bbdabaa
aaab=bdaaca
abaabc=baacab
aacabd=bbdabaab
abaabb=caaa
aacabb=bbaaac
aacaad=bbdaabaa
aacaabd=bbdaabaab
aacaabb=bbdacaaac
aacaaa=bbd

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#686 ⟨a, b | aabbbaaab=1⟩

Properties

Complete rewriting system

Right Cayley graph (truncated)

Left Cayley graph (truncated)