#4268 ⟨a, b | abaababba=ab⟩

Contents

Properties
Rewriting system

Properties

Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by d is not injective:
- d ⋅ a²da = d and d ⋅ 1 = d, 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 = ba
2. d = cbb
Reduction order:
- Right-to-left 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.	acda ⇒ acad	[12]
2.	c²da ⇒ c²ad	[13]
3.	dc ⇒ c²ac²d	[18]
4.	acada² ⇒ ac	[7]
5.	c²ada² ⇒ c²	[9]
6.	c²adac ⇒ da	[8]
7.	ab ⇒ acada	[4]
8.	cb ⇒ c²ada	[6]
9.	ba ⇒ c	[2]
10.	d²a ⇒ dad	[16]
11.	(da)² ⇒ da²d	[15]
12.	da²da ⇒ d	[11]
13.	dacadac ⇒ c²d	[17]
14.	db ⇒ (c²a)²dad	[19]

# ab:abaababba=ab reversed:ac/db ba=c,cbb=d morph:2/1,3/1
acda=acad
ccda=ccad
dc=ccaccd
acadaa=ac
ccadaa=cc
ccadac=da
ab=acada
cb=ccada
ba=c
dda=dad
dada=daad
daada=d
dacadac=ccd
db=ccaccadad