#4807 ⟨a, b | abaabbba=baa⟩

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 a is not injective:
- ba ⋅ a = aca and ac ⋅ a = aca, however ba ≠ ac

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

#	Rule	Proof
1.	aca²c³a ⇒ ca²	[14]
2.	aca²c⁴ ⇒ cac	[12]
3.	acad ⇒ c	[5]
4.	dc ⇒ ac⁴ad	[11]
5.	da² ⇒ ac³a	[13]
6.	dac ⇒ ac⁴	[9]
7.	bc ⇒ ac²ad	[10]
8.	ba² ⇒ aca	[4]
9.	bac ⇒ ac²	[8]
10.	bd ⇒ db	[6]
11.	b³ ⇒ d	[3]

# ab:abaabbba=baa reversed:ac/d/b baabbb=c,bbb=d morph:6/1,3/1
acaaccca=caa
acaacccc=cac
acad=c
dc=accccad
daa=accca
dac=acccc
bc=accad
baa=aca
bac=acc
bd=db
bbb=d