#1521 ⟨a, b | ababbabbba=1⟩

Properties

Presentation has sum-of-sides 10
Infinite non-Abelian group
Group inverses:
- a^-1 = bdb²a
- b^-1 = db²c
- c^-1 = bdb²
- d^-1 = b²cb

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

cbdb ⇒ db²c
bcbd ⇒ db²c
bdb²c ⇒ 1
db²cb ⇒ 1
db²c²bd ⇒ cbd²b²c
(db²c)² ⇒ cbd
ac ⇒ ca
ad ⇒ cb²ab
abc ⇒ cb(b²c)²bab
ab² ⇒ d²b²a
abd ⇒ b³cba
a² ⇒ c

# ab:ababbabbba=1 reversed:cbd/a aa=c,abbab=d frequency:2/3,5/1
cbdb=dbbc
bcbd=dbbc
bdbbc=1
dbbcb=1
dbbccbd=cbddbbc
dbbcdbbc=cbd
ac=ca
ad=cbbab
abc=cbbbcbbcbab
abb=ddbba
abd=bbbcba
aa=c

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#1521 ⟨a, b | ababbabbba=1⟩

Properties

Complete rewriting system

Right Cayley graph (truncated)

Left Cayley graph (truncated)