#1053 ⟨a, b | aaabba=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:
- a³b² ⋅ a = ba² and ba ⋅ a = ba², however a³b² ≠ 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 = bb
2. d = caa
Reduction order:
- Right-to-left recursive path with deg(a) = deg(d) = 0, a < d; deg(c) = deg(b) = 1, c < b
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	a³d² ⇒ da	[11]
2.	a³dca ⇒ d	[6]
3.	cd ⇒ dadca	[8]
4.	ca² ⇒ d	[3]
5.	cad ⇒ da²dca	[9]
6.	bd ⇒ daca	[7]
7.	ba² ⇒ a³ca	[4]
8.	bad ⇒ a³dadca	[10]
9.	cb ⇒ bc	[5]
10.	b² ⇒ c	[2]

# ab:aaabba=baa reversed:ad/cb bb=c,caa=d morph:2/1,3/0
aaadd=da
aaadca=d
cd=dadca
caa=d
cad=daadca
bd=daca
baa=aaaca
bad=aaadadca
cb=bc
bb=c