#4711 ⟨a, b | aabbabba=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:
- a(ab²)² ⋅ a = ba² and ba ⋅ a = ba², however a(ab²)² ≠ ba

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 = bba
2. d = cccc
3. e = da
Reduction order:
- Right-to-left recursive path with deg(a) = deg(e) = 0, a < e; deg(d) = 1; deg(c) = 2; deg(b) = 3
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	a²e⁴ ⇒ ea	[13]
2.	a²e³d ⇒ e	[9]
3.	da ⇒ e	[4]
4.	de ⇒ eae³d	[10]
5.	ca ⇒ a²d	[8]
6.	ce ⇒ ead	[14]
7.	cd ⇒ dc	[6]
8.	c⁴ ⇒ d	[3]
9.	be ⇒ a(ae)²(eae³)²d²	[11]
10.	ba² ⇒ a²c²	[5]
11.	bae ⇒ a⁴e(eae³)³d²	[12]
12.	b²a ⇒ c	[2]

# ab:aabbabba=baa reversed:ae/d/c/b bba=c,cccc=d,da=e morph:3/0,4/0,2/1
aaeeee=ea
aaeeed=e
da=e
de=eaeeed
ca=aad
ce=ead
cd=dc
cccc=d
be=aaeaeeaeeeeaeeedd
baa=aacc
bae=aaaaeeaeeeeaeeeeaeeedd
bba=c