#3783 ⟨a, b | ababbabaab=a⟩

Contents

Properties
Rewriting system

Properties

Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element b has infinite order
Not left cancellative, because left multiplication by c is not injective:
- c ⋅ db² = c and c ⋅ 1 = c, however db² ≠ 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 = cbcaa
Reduction order:
- Right-to-left recursive path with deg(b) = deg(c) = 0, b < c; deg(d) = deg(a) = 1, d < a
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	dc ⇒ cbc⁴d	[14]
2.	cdb² ⇒ c	[5]
3.	c³dbc ⇒ c²bc²d	[11]
4.	cbc²dbc ⇒ db	[7]
5.	a ⇒ cdb	[4]
6.	d²b ⇒ dbd	[10]
7.	(db)² ⇒ d	[8]
8.	(dbc)² ⇒ db²c²d	[13]
9.	dbc²dbc ⇒ dbcbc²d	[12]
10.	db²c²dbc ⇒ cbc²d	[9]

# ab:ababbabaab=a reversed:bc/da ab=c,cbcaa=d morph:2/0,5/0
dc=cbccccd
cdbb=c
cccdbc=ccbccd
cbccdbc=db
a=cdb
ddb=dbd
dbdb=d
dbcdbc=dbbccd
dbccdbc=dbcbccd
dbbccdbc=cbccd