#2184 ⟨a, b | aaabbaa=aab⟩

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Properties
Rewriting system

Properties

Presentation has sum-of-sides 10
Infinite non-cancellative non-commutative monoid
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ a²b²a² = a²b and a ⋅ ab = a²b, however a²b²a² ≠ ab
Enveloping group: ⟨a, b | aabab^-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 = bbaa
Reduction order:
- Left-to-right 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.	(ca)³a ⇒ c²	[7]
2.	c³aca² ⇒ c(ac)³	[10]
3.	a³caca² ⇒ a²c	[6]
4.	a²c²aca² ⇒ a²(ac)³	[9]
5.	ca(ac)²a² ⇒ cac	[8]
6.	(cac)²a² ⇒ ca(ac)³	[11]
7.	cb ⇒ cac	[4]
8.	a²b ⇒ a³c	[3]
9.	cab ⇒ ca²c	[5]
10.	b²a² ⇒ c	[2]

# ab:aaabbaa=aab ac/b bbaa=c morph:4/0
cacacaa=cc
cccacaa=cacacac
aaacacaa=aac
aaccacaa=aaacacac
caacacaa=cac
caccacaa=caacacac
cb=cac
aab=aaac
cab=caac
bbaa=c