#1804 ⟨a, b | abbaabaab=b⟩

Contents

Properties
Rewriting system

Properties

Sum of relation sides is 10
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not right cancellative, because right multiplication by c is not injective:
- a²da ⋅ c = c and 1 ⋅ c = c, however a²da ≠ 1

Rewriting system

Format:	Pretty Plain
Word:
	Enter a word above to compute its normal form. Tips: Lowercase letters stand for generators. Spaces are ignored. Numbers repeat the previous letter, e.g. `b90`.
Strategy:	Leftmost Rightmost
Result:	1 1

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

#	Rule	Proof
1.	adc ⇒ dac	[13]
2.	cd ⇒ d(cac)²	[17]
3.	a²dac ⇒ c	[9]
4.	cadac² ⇒ dc(ac)²	[18]
5.	cad(ac)² ⇒ ad	[11]
6.	b ⇒ adac	[7]
7.	ad² ⇒ dad	[16]
8.	(ad)² ⇒ da²d	[14]
9.	ada²d ⇒ d	[10]
10.	cadacad ⇒ dcaca²d	[19]
11.	cadaca²d ⇒ dcac	[20]

# ab:abbaabaab=b ac/db ab=c,bbac=d morph:2/0,4/1
adc=dac
cd=dcaccac
aadac=c
cadacc=dcacac
cadacac=ad
b=adac
add=dad
adad=daad
adaad=d
cadacad=dcacaad
cadacaad=dcac