#1073 ⟨a, b | aababa=baa⟩

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Properties
Rewriting system

Properties

Presentation has sum-of-sides 9
Infinite non-cancellative non-commutative monoid
Not right cancellative, because right multiplication by a is not injective:
- a(ab)² ⋅ a = ba² and ba ⋅ a = ba², however a(ab)² ≠ ba
Enveloping group: ⟨a, b | aabba^-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 = baa
2. d = aba
Reduction order:
- Right-to-left recursive path with deg(a) = deg(d) = deg(c) = 0, a < d < c; deg(b) = 1
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	ac ⇒ da	[8]
2.	adc ⇒ ca	[10]
3.	aba ⇒ d	[3]
4.	adba ⇒ c	[5]
5.	abd ⇒ dba	[6]
6.	adbd ⇒ cba	[11]
7.	bc ⇒ cbd	[12]
8.	ba² ⇒ c	[2]
9.	bda ⇒ cdba	[9]
10.	bad ⇒ cba	[7]
11.	bd² ⇒ cdbd	[13]
12.	bdc ⇒ cdcbd	[14]

# ab:aababa=baa reversed:adc/b baa=c,aba=d morph:3/1,3/0
ac=da
adc=ca
aba=d
adba=c
abd=dba
adbd=cba
bc=cbd
baa=c
bda=cdba
bad=cba
bdd=cdbd
bdc=cdcbd