#158 ⟨a, b | abbaaab=1⟩

Properties

Presentation has sum-of-sides 7
Infinite non-Abelian group
Group inverses:
- a^-1 = da²
- b^-1 = bcba
- 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(a) = 0, c < d < a; deg(b) = 1
Auxiliary generator: aaa=c
Auxiliary generator: babb=d

cd ⇒ 1
dc ⇒ 1
ac ⇒ ca
ad ⇒ da
a³ ⇒ c
cbab ⇒ bcba
dbcb ⇒ babda²
ab² ⇒ bcbda
c(ab)² ⇒ abcba
dabcb ⇒ (ab)²da²
a²bcb ⇒ cb²a²
a(ab)² ⇒ b²c
b²cb ⇒ da²

# ab:abbaaab=1 cda/b aaa=c,babb=d magic:0
cd=1
dc=1
ac=ca
ad=da
aaa=c
cbab=bcba
dbcb=babdaa
abb=bcbda
cabab=abcba
dabcb=ababdaa
aabcb=cbbaa
aabab=bbc
bbcb=daa

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#158 ⟨a, b | abbaaab=1⟩

Properties

Complete rewriting system

Right Cayley graph (truncated)

Left Cayley graph (truncated)