#4306 ⟨a, b | ababbaaab=aa⟩

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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(c) = deg(a) = 0, c < a; deg(b) = 1
Auxiliary generators:
1. babba=c
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	(c²a)²ac ⇒ ca²	[11]
2.	acac²a²c ⇒ a³	[10]
3.	ca³c²a²c ⇒ c²ac²a⁴	[15]
4.	a⁴c²a²c ⇒ acac²a⁴	[14]
5.	caba ⇒ c³a²c	[9]
6.	a²ba ⇒ ac²a²c	[8]
7.	c²a²b ⇒ ca	[5]
8.	aca²b ⇒ a²	[3]
9.	ca⁴b ⇒ c²ac²a³	[12]
10.	a⁵b ⇒ acac²a³	[13]
11.	cb²a ⇒ babc	[4]
12.	ca²b²a ⇒ c²a²c	[7]
13.	a³b²a ⇒ aca²c	[6]
14.	bab²a ⇒ c	[2]

# ab:ababbaaab=aa ca/b babba=c morph:5/1
ccaccaac=caa
acaccaac=aaa
caaaccaac=ccaccaaaa
aaaaccaac=acaccaaaa
caba=cccaac
aaba=accaac
ccaab=ca
acaab=aa
caaaab=ccaccaaa
aaaaab=acaccaaa
cbba=babc
caabba=ccaac
aaabba=acaac
babba=c