#2171 ⟨a, b | aaababa=baa⟩

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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:
- a³bab ⋅ a = ba² and ba ⋅ a = ba², however a³bab ≠ ba
Enveloping group: ⟨a, b | aaabba^-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 = aaabab
Reduction order:
- Right-to-left recursive path with deg(a) = deg(c) = 0, a < c; deg(b) = 1
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	a³c²a ⇒ ca²	[17]
2.	a³c³ ⇒ cac	[7]
3.	a³cbc ⇒ c²	[11]
4.	a³c²bc ⇒ cabc	[12]
5.	ba² ⇒ ca	[3]
6.	bac ⇒ c²	[6]
7.	bc² ⇒ ca²cbc	[13]
8.	bca² ⇒ ca²c²a	[8]
9.	bcac ⇒ ca²c³	[9]
10.	a³bab ⇒ c	[2]
11.	ca(ab)² ⇒ bc	[5]
12.	b²c ⇒ ca²c²(ab)²	[16]
13.	babc ⇒ cbc	[10]
14.	(bc)² ⇒ c(a²c²)²(ab)²	[15]
15.	bcabc ⇒ ca²c²bc	[14]

# ab:aaababa=baa reversed:ac/b aaabab=c morph:6/0
aaacca=caa
aaaccc=cac
aaacbc=cc
aaaccbc=cabc
baa=ca
bac=cc
bcc=caacbc
bcaa=caacca
bcac=caaccc
aaabab=c
caabab=bc
bbc=caaccabab
babc=cbc
bcbc=caaccaaccabab
bcabc=caaccbc