#22256 ⟨a, b | aaa=1, abaaba=bb⟩

Quick links

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

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

#	Rule	Proof
1.	a³ ⇒ 1	[1]
2.	b² ⇒ ca²	[4]
3.	ba²b ⇒ a²ca	[8]
4.	aba²c ⇒ ba²ca²	[20]
5.	cb ⇒ abaca	[9]
6.	cab ⇒ ba²ca	[12]
7.	ca²b ⇒ bca²	[5]
8.	(ac)² ⇒ c²a²	[17]
9.	a²c² ⇒ (ca)²	[14]
10.	abcac ⇒ ba²(ca²)²	[22]
11.	abac² ⇒ bcaca²	[16]
12.	ac³ ⇒ c³a	[18]
13.	abc³ ⇒ bca(ca²)²	[23]

# ab:aaa=1,abaaba=bb a/bc bba=c morph:3/0
aaa=1
bb=caa
baab=aaca
abaac=baacaa
cb=abaca
cab=baaca
caab=bcaa
acac=ccaa
aacc=caca
abcac=baacaacaa
abacc=bcacaa
accc=ccca
abccc=bcacaacaa