#4536 ⟨a, b | aaabbaaa=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. bbaaa=c
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	(ca)³a² ⇒ c²	[7]
2.	c³aca³ ⇒ (ca)³ac	[11]
3.	a³caca³ ⇒ a²c	[6]
4.	a²c²aca³ ⇒ a³caca²c	[10]
5.	ca(ac)²a³ ⇒ cac	[8]
6.	(cac)²a³ ⇒ ca(ac)²a²c	[12]
7.	cb ⇒ cac	[4]
8.	a²b ⇒ a³c	[3]
9.	cab ⇒ ca²c	[5]
10.	b²a³ ⇒ c	[2]
11.	b²a²c ⇒ c²aca³	[9]

# ab:aaabbaaa=aab ac/b bbaaa=c morph:5/0
cacacaaa=cc
cccacaaa=cacacaac
aaacacaaa=aac
aaccacaaa=aaacacaac
caacacaaa=cac
caccacaaa=caacacaac
cb=cac
aab=aaac
cab=caac
bbaaa=c
bbaac=ccacaaa