#945 ⟨a, b | aababba=ab⟩

Quick links

Properties
Rewriting system

Properties

Presentation has sum-of-sides 9
Infinite non-cancellative non-commutative monoid
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ abab²a = ab and a ⋅ b = ab, however abab²a ≠ b
Enveloping group: ⟨a, b | aabab^-1b^-1⟩

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

#	Rule	Proof
1.	a²bc² ⇒ cb	[4]
2.	cabca ⇒ cb	[7]
3.	ab² ⇒ c	[2]
4.	cbabc² ⇒ cabc²b	[12]
5.	cb²ca ⇒ cabcb	[14]
6.	cb³ ⇒ cabc²	[8]
7.	a²bca ⇒ ab	[3]
8.	a²bcb ⇒ c²a	[10]
9.	(ab)²c² ⇒ cb²	[6]
10.	cbabca ⇒ cb²	[9]
11.	cbabcb ⇒ cabc³a	[15]
12.	cb²abc² ⇒ cabc²b²	[16]
13.	(ab)²ca ⇒ c	[5]
14.	(ab)²cb ⇒ cbca	[11]
15.	cb²abca ⇒ cabc²	[13]
16.	cb²abcb ⇒ cabc²bca	[17]

# ab:aababba=ab c/ab abb=c morph:3/0
aabcc=cb
cabca=cb
abb=c
cbabcc=cabccb
cbbca=cabcb
cbbb=cabcc
aabca=ab
aabcb=cca
ababcc=cbb
cbabca=cbb
cbabcb=cabccca
cbbabcc=cabccbb
ababca=c
ababcb=cbca
cbbabca=cabcc
cbbabcb=cabccbca