#1916 ⟨a, b | aaabbaba=ab⟩

Quick links

Properties
Rewriting system

Properties

Presentation has sum-of-sides 10
Infinite non-cancellative non-commutative monoid
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ a²b(ba)² = ab and a ⋅ b = ab, however a²b(ba)² ≠ b
Enveloping group: ⟨a, b | aababa^-1bb⟩

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 = ab
Reduction order:
- Left-to-right recursive path with deg(a) = deg(c) = 0, a < c; deg(b) = 1
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	ab ⇒ c	[2]
2.	a²cbca ⇒ c	[4]
3.	a²cbc² ⇒ cb	[5]
4.	cacbca ⇒ cb	[6]
5.	cb² ⇒ cacbc²	[7]
6.	cbacbca ⇒ cacbc²	[9]
7.	a²(cb)² ⇒ c²bca	[8]
8.	ca(cb)² ⇒ c(bc)²a	[11]
9.	cacbc²b ⇒ cbacbc²	[10]
10.	cba(cb)² ⇒ cacbc³bca	[12]
11.	cbacbc²b ⇒ c(acbc²)²	[13]

# ab:aaabbaba=ab ac/b ab=c magic:0
ab=c
aacbca=c
aacbcc=cb
cacbca=cb
cbb=cacbcc
cbacbca=cacbcc
aacbcb=ccbca
cacbcb=cbcbca
cacbccb=cbacbcc
cbacbcb=cacbcccbca
cbacbccb=cacbccacbcc