#1808 ⟨a, b | abbabaaab=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:
- a²da² ⋅ c = c and 1 ⋅ c = c, however a²da² ≠ 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 = 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	[15]
2.	adac ⇒ da²c	[12]
3.	cd ⇒ dc²a²c²	[18]
4.	a²da²c ⇒ c	[9]
5.	cada²c² ⇒ ad	[11]
6.	b ⇒ ada²c	[7]
7.	ad² ⇒ dad	[17]
8.	(ad)² ⇒ da²d	[16]
9.	ada²d ⇒ da³d	[13]
10.	ada³d ⇒ d	[10]
11.	cada²cad ⇒ dc²	[19]

# ab:abbabaaab=b ac/db ab=c,bbc=d morph:2/0,3/0
adc=dac
adac=daac
cd=dccaacc
aadaac=c
cadaacc=ad
b=adaac
add=dad
adad=daad
adaad=daaad
adaaad=d
cadaacad=dcc