#1245 ⟨a, b | abaab=abba⟩

Properties

Presentation has sum-of-sides 9
Infinite non-commutative monoid

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 shortlex with a < b < c
Auxiliary generator: bb=c

b² ⇒ c
cb ⇒ bc
aba²b ⇒ aca
aba²c ⇒ acab
aca³b ⇒ acaba
ac(ab)² ⇒ aca³c
acaba³b ⇒ aca³ca
acaba³c ⇒ aca³cab
(aca²)²b ⇒ acabaca
(aca²)²c ⇒ (acab)²

# ab:abaab=abba abc bb=c frequency:2/3
bb=c
cb=bc
abaab=aca
abaac=acab
acaaab=acaba
acabab=acaaac
acabaaab=acaaaca
acabaaac=acaaacab
acaaacaab=acabaca
acaaacaac=acabacab

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#1245 ⟨a, b | abaab=abba⟩

Properties

Complete rewriting system

Right Cayley graph (truncated)

Left Cayley graph (truncated)