#4631 ⟨a, b | aabaabba=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 = ada and ad ⋅ a = ada, however ba ≠ ad

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

#	Rule	Proof
1.	(a²d)²da ⇒ da²	[13]
2.	a²da²d³ ⇒ dad	[11]
3.	a²dac ⇒ d	[5]
4.	cd ⇒ ad(da)²c	[14]
5.	ca² ⇒ ad²a	[12]
6.	cad ⇒ ad³	[10]
7.	bd ⇒ a(da)²c	[8]
8.	ba² ⇒ ada	[4]
9.	bad ⇒ ad²	[9]
10.	bc ⇒ cb	[6]
11.	b² ⇒ c	[2]

# ab:aabaabba=baa reversed:ad/c/b bb=c,abaac=d morph:2/1,5/1
aadaadda=daa
aadaaddd=dad
aadac=d
cd=addadac
caa=adda
cad=addd
bd=adadac
baa=ada
bad=add
bc=cb
bb=c