#1391 ⟨a, b | aabaaaaaab=1⟩

Properties

Presentation has sum-of-sides 10
Infinite non-Abelian group
Group inverses:
- a^-1 = da⁵
- b^-1 = dba²c²
- 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(a) = deg(c) = 0, d < a < c; deg(b) = 1
Auxiliary generator: aaaaaa=c
Auxiliary generator: baab=d

dc ⇒ 1
ad ⇒ da
cd ⇒ 1
ca ⇒ ac
dac ⇒ a
da²c ⇒ a²
da³c ⇒ a³
da⁴c ⇒ a⁴
a⁶ ⇒ c
da⁵c ⇒ a⁵
cb ⇒ dbc²
d²b ⇒ bd²
a²b ⇒ dba²c
d²ab ⇒ abd²
bdb ⇒ d³a⁴

# ab:aabaaaaaab=1 dac/b aaaaaa=c,baab=d magic:0
dc=1
ad=da
cd=1
ca=ac
dac=a
daac=aa
daaac=aaa
daaaac=aaaa
aaaaaa=c
daaaaac=aaaaa
cb=dbcc
ddb=bdd
aab=dbaac
ddab=abdd
bdb=dddaaaa

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#1391 ⟨a, b | aabaaaaaab=1⟩

Properties

Complete rewriting system

Right Cayley graph (truncated)

Left Cayley graph (truncated)