#1437 ⟨a, b | aabbaaaaab=1⟩

Properties

Presentation has sum-of-sides 10
Infinite non-Abelian group
Group inverses:
- a^-1 = da⁴
- b^-1 = bcba²
- 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: aaaaa=c
Auxiliary generator: baabb=d

cd ⇒ 1
dc ⇒ 1
ac ⇒ ca
ad ⇒ da
a⁵ ⇒ c
cba²b ⇒ bcba²
dbcb ⇒ ba²bda³
caba²b ⇒ abcba²
dabcb ⇒ aba²bda³
a²b² ⇒ bcbda²
c(a²b)² ⇒ a²bcba²
da²bcb ⇒ (a²b)²da³
a³bcb ⇒ cb²a³
a(a²b)² ⇒ b²c
b²cb ⇒ da³

# ab:aabbaaaaab=1 cda/b aaaaa=c,baabb=d magic:0
cd=1
dc=1
ac=ca
ad=da
aaaaa=c
cbaab=bcbaa
dbcb=baabdaaa
cabaab=abcbaa
dabcb=abaabdaaa
aabb=bcbdaa
caabaab=aabcbaa
daabcb=aabaabdaaa
aaabcb=cbbaaa
aaabaab=bbc
bbcb=daaa

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#1437 ⟨a, b | aabbaaaaab=1⟩

Properties

Complete rewriting system

Right Cayley graph (truncated)

Left Cayley graph (truncated)