#2431 ⟨a, b | aaabaa=baba⟩

Properties

Presentation has sum-of-sides 10
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:
- Right-to-left recursive path with deg(c) = 0; deg(a) = deg(b) = 1, a < b
Auxiliary generator: ba=c

ba ⇒ c
bcbc² ⇒ ca²c³
ca²ca ⇒ bc²
a³c³ ⇒ cbc²
ca²bc² ⇒ bc(ca)²
ca²c²bc² ⇒ bc²a²c³
a³ca ⇒ c²
a³bc² ⇒ c(ca)²
a³c²bc² ⇒ c²a²c³

# ab:aaabaa=baba reversed:c/ab ba=c frequency:2/0
ba=c
bcbcc=caaccc
caaca=bcc
aaaccc=cbcc
caabcc=bccaca
caaccbcc=bccaaccc
aaaca=cc
aaabcc=ccaca
aaaccbcc=ccaaccc

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#2431 ⟨a, b | aaabaa=baba⟩

Properties

Complete rewriting system

Right Cayley graph (truncated)

Left Cayley graph (truncated)