#1544 ⟨a, b | abbbabbbba=1⟩

Properties

Presentation has sum-of-sides 10
Infinite non-Abelian group
Group inverses:
- a^-1 = ab³ac
- b^-1 = db³
- 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(b) = 0, c < d < b; deg(a) = 1
Auxiliary generator: bbbb=c
Auxiliary generator: aabbba=d

cd ⇒ 1
dc ⇒ 1
bc ⇒ cb
bd ⇒ db
b⁴ ⇒ c
ca² ⇒ ab³ab
dab³a ⇒ a²db³
ba² ⇒ acadb
bab³a ⇒ (ca)²d
b³aca ⇒ ab³ac
a²b³a ⇒ d
dab²aca ⇒ a²db³ab³
dacb²aca ⇒ a²b²ac
bab²aca ⇒ (ca)²dab³
bacb²aca ⇒ (ca)²db³ac
a²b²aca ⇒ dab³
a²cb²aca ⇒ db³ac

# ab:abbbabbbba=1 cdb/a bbbb=c,aabbba=d magic:1
cd=1
dc=1
bc=cb
bd=db
bbbb=c
caa=abbbab
dabbba=aadbbb
baa=acadb
babbba=cacad
bbbaca=abbbac
aabbba=d
dabbaca=aadbbbabbb
dacbbaca=aabbac
babbaca=cacadabbb
bacbbaca=cacadbbbac
aabbaca=dabbb
aacbbaca=dbbbac

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#1544 ⟨a, b | abbbabbbba=1⟩

Properties

Complete rewriting system

Right Cayley graph (truncated)

Left Cayley graph (truncated)