#812 ⟨a, b | aabbaaab=a⟩

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 ⋅ ab²a³b = a and a ⋅ 1 = a, however ab²a³b ≠ 1
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 = aaa
Reduction order:
- Left-to-right recursive path with deg(b) = deg(c) = 0, b < c; deg(a) = 1
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	c²b²cb ⇒ cb(bc)²	[12]
2.	c²(bcb)² ⇒ c²b³cbc	[15]
3.	(cb)³bcb ⇒ cbcb³cbc	[13]
4.	(cb²cb)² ⇒ c(b²cb)²c	[10]
5.	c²b³c(bcb)² ⇒ cbcb³cbcb²c	[16]
6.	cbcb³c(bcb)² ⇒ c(b²cb)²cb²c	[14]
7.	cb²cb³c(bcb)² ⇒ c	[11]
8.	a ⇒ c(b²cb)²	[9]

# ab:aabbaaab=a bc/a aaa=c morph:3/0
ccbbcb=cbbcbc
ccbcbbcb=ccbbbcbc
cbcbcbbcb=cbcbbbcbc
cbbcbcbbcb=cbbcbbbcbc
ccbbbcbcbbcb=cbcbbbcbcbbc
cbcbbbcbcbbcb=cbbcbbbcbcbbc
cbbcbbbcbcbbcb=c
a=cbbcbbbcb