#2431 ⟨a, b | aaabaa=baba⟩

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Properties
Rewriting system

Properties

Presentation has sum-of-sides 10
Infinite non-cancellative non-commutative monoid
Not right cancellative, because right multiplication by a is not injective:
- a³ba ⋅ a = (ba)² and bab ⋅ a = (ba)², however a³ba ≠ bab
Enveloping group: ⟨a, b | aaabab^-1b^-1⟩

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

Auxiliary generators:
1. c = ba
Reduction order:
- Right-to-left recursive path with deg(c) = 0; deg(a) = deg(b) = 1, a < b
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	ba ⇒ c	[2]
2.	bcbc² ⇒ ca²c³	[8]
3.	ca²ca ⇒ bc²	[5]
4.	a³c³ ⇒ cbc²	[6]
5.	ca²bc² ⇒ bc(ca)²	[9]
6.	ca²c²bc² ⇒ bc²a²c³	[11]
7.	a³ca ⇒ c²	[4]
8.	a³bc² ⇒ c(ca)²	[7]
9.	a³c²bc² ⇒ c²a²c³	[10]

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