#1518 ⟨a, b | ababbaabab=1⟩

Properties

Presentation has sum-of-sides 10
Infinite non-Abelian group
Group inverses:
- a^-1 = bdc³
- b^-1 = ac⁴
- c^-1 = dc³
- d^-1 = c⁴

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

cd ⇒ dc
dc⁴ ⇒ 1
da ⇒ ac¹⁶
ca ⇒ ad
db ⇒ bc
dcb ⇒ cbc
dc²b ⇒ c²bc
dc³b ⇒ c³bc
c⁴b ⇒ bdc³
ab ⇒ c
ba ⇒ d

# ab:ababbaabab=1 dc/ab ab=c,ba=d frequency:2/0,2/1
cd=dc
dcccc=1
da=acccccccccccccccc
ca=ad
db=bc
dcb=cbc
dccb=ccbc
dcccb=cccbc
ccccb=bdccc
ab=c
ba=d

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#1518 ⟨a, b | ababbaabab=1⟩

Properties

Complete rewriting system

Right Cayley graph (truncated)

Left Cayley graph (truncated)