#5211 ⟨a, b | aabbaab=abaa⟩

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

#	Rule	Proof
1.	cb²a ⇒ ab²c	[4]
2.	ab²a ⇒ c	[2]
3.	cba² ⇒ c²ab	[5]
4.	c(cab)² ⇒ c³a	[9]
5.	c²ab³a ⇒ cbac	[8]
6.	c³aba ⇒ c²abc²	[10]
7.	c³acab ⇒ c²abc²a	[13]
8.	aba² ⇒ acab	[3]
9.	a(cab)² ⇒ ac²a	[7]
10.	acab³a ⇒ abac	[6]
11.	ac²aba ⇒ acabc²	[14]
12.	ac(ca)²b ⇒ acabc²a	[12]
13.	(c²ab)²a ⇒ c³ac²	[17]
14.	c²abc(ca)²b ⇒ c(c²a)²	[19]
15.	c³a³ ⇒ c²ab(ca)²b	[11]
16.	acabc²aba ⇒ (ac²)²	[16]
17.	acabc(ca)²b ⇒ a(c²a)²	[20]
18.	ac²a³ ⇒ acab(ca)²b	[15]
19.	c²abc²a³ ⇒ c²(ca)³b	[18]
20.	acabc²a³ ⇒ ac(ca)³b	[21]

# ab:aabbaab=abaa bc/a abba=c morph:4/3
cbba=abbc
abba=c
cbaa=ccab
ccabcab=ccca
ccabbba=cbac
cccaba=ccabcc
cccacab=ccabcca
abaa=acab
acabcab=acca
acabbba=abac
accaba=acabcc
accacab=acabcca
ccabccaba=cccacc
ccabccacab=cccacca
cccaaa=ccabcacab
acabccaba=accacc
acabccacab=accacca
accaaa=acabcacab
ccabccaaa=cccacacab
acabccaaa=accacacab