#3813 ⟨a, b | abbabaaaab=b⟩

Contents

Properties
Rewriting system

Properties

Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not right cancellative, because right multiplication by c is not injective:
- ad ⋅ c = dac and da ⋅ c = dac, however ad ≠ da

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 = bbc
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	[17]
2.	adac ⇒ da²c	[15]
3.	ada²c ⇒ da³c	[12]
4.	cd ⇒ dc²a³c²	[21]
5.	a²da³c ⇒ c	[9]
6.	cada³c² ⇒ ad	[11]
7.	b ⇒ ada³c	[7]
8.	ad² ⇒ dad	[19]
9.	(ad)² ⇒ da²d	[18]
10.	ada²d ⇒ da³d	[16]
11.	ada³d ⇒ da⁴d	[13]
12.	ada⁴d ⇒ d	[10]
13.	cada³cad ⇒ dc²	[20]

# ab:abbabaaaab=b ac/db ab=c,bbc=d morph:2/0,3/0
adc=dac
adac=daac
adaac=daaac
cd=dccaaacc
aadaaac=c
cadaaacc=ad
b=adaaac
add=dad
adad=daad
adaad=daaad
adaaad=daaaad
adaaaad=d
cadaaacad=dcc