#4711 ⟨a, b | aabbabba=baa⟩

Quick links

Properties
Rewriting system

Properties

Presentation has sum-of-sides 11
Infinite non-commutative monoid

Rewriting system

Format:	Pretty Plain
Word to reduce:
	Tips: Lowercase letters stand for generators. Spaces are ignored. Numbers repeat the previous letter, e.g. `b90`.
Reduction strategy:	Leftmost Rightmost
Path to normal form:	1 1

Reduction order:
- Right-to-left recursive path with deg(a) = deg(e) = 0, a < e; deg(d) = 1; deg(c) = 2; deg(b) = 3
Auxiliary generators:
1. bba=c
2. cccc=d
3. da=e
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