#5551 ⟨a, b | aaabaa=baaba⟩

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Properties
Rewriting system

Properties

Presentation has sum-of-sides 11
Infinite non-cancellative non-commutative monoid
Not right cancellative, because right multiplication by a is not injective:
- a³ba ⋅ a = ba²ba and ba²b ⋅ a = ba²ba, however a³ba ≠ ba²b
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 = aaba
Reduction order:
- Right-to-left shortlex with b < a < c
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	aca ⇒ bc	[4]
2.	a²ba ⇒ c	[2]
3.	a²bc ⇒ caba	[6]
4.	acbc ⇒ bc²a	[5]
5.	bcaba ⇒ ac²	[8]
6.	a²b²c ⇒ c²a	[7]
7.	a³c² ⇒ cabc	[10]
8.	ac²aba ⇒ bcabc	[9]
9.	bcab²c ⇒ ac³a	[11]
10.	bca²c² ⇒ ac²abc	[12]
11.	ac²ab²c ⇒ bcabc²a	[13]
12.	bc(abc)² ⇒ ac²a²c²	[14]

# ab:aaabaa=baaba reversed:bac aaba=c morph:4/0
aca=bc
aaba=c
aabc=caba
acbc=bcca
bcaba=acc
aabbc=cca
aaacc=cabc
accaba=bcabc
bcabbc=accca
bcaacc=accabc
accabbc=bcabcca
bcabcabc=accaacc