#4508 ⟨a, b | aaababaa=aab⟩

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Properties
Rewriting system

Properties

Presentation has sum-of-sides 11
Infinite non-commutative monoid

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

Reduction order:
- Left-to-right recursive path with deg(a) = deg(c) = 0, a < c; deg(b) = 1
Auxiliary generators:
1. babaa=c
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	c³a² ⇒ c(ac)²	[10]
2.	a²c²a² ⇒ a³cac	[9]
3.	cac²a² ⇒ ca(ac)²	[11]
4.	ca(ca²)² ⇒ c²	[7]
5.	a³(ca²)² ⇒ a²c	[6]
6.	(ca²)³ ⇒ cac	[8]
7.	cb ⇒ cac	[4]
8.	a²b ⇒ a³c	[3]
9.	cab ⇒ ca²c	[5]
10.	baba² ⇒ c	[2]

# ab:aaababaa=aab ac/b babaa=c morph:5/0
cccaa=cacac
aaccaa=aaacac
caccaa=caacac
cacaacaa=cc
aaacaacaa=aac
caacaacaa=cac
cb=cac
aab=aaac
cab=caac
babaa=c