#338 ⟨a, b | abbabbba=1⟩

Properties

Presentation has sum-of-sides 8
Infinite non-Abelian group
Group inverses:
- a^-1 = ab²ac
- b^-1 = db²
- 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: bbb=c
Auxiliary generator: aabba=d

cd ⇒ 1
dc ⇒ 1
bc ⇒ cb
bd ⇒ db
b³ ⇒ c
ca² ⇒ ab²ab
dab²a ⇒ a²db²
ba² ⇒ acadb
bab²a ⇒ (ca)²d
b²aca ⇒ ab²ac
a²b²a ⇒ d
dabaca ⇒ a²db²ab²
dacbaca ⇒ a²bac
(ba)²ca ⇒ (ca)²dab²
(bac)²a ⇒ (ca)²db²ac
a²baca ⇒ dab²
a²cbaca ⇒ db²ac

# ab:abbabbba=1 cdb/a bbb=c,aabba=d magic:1
cd=1
dc=1
bc=cb
bd=db
bbb=c
caa=abbab
dabba=aadbb
baa=acadb
babba=cacad
bbaca=abbac
aabba=d
dabaca=aadbbabb
dacbaca=aabac
babaca=cacadabb
bacbaca=cacadbbac
aabaca=dabb
aacbaca=dbbac

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#338 ⟨a, b | abbabbba=1⟩

Properties

Complete rewriting system

Right Cayley graph (truncated)

Left Cayley graph (truncated)