#4647 ⟨a, b | aabababa=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 = da and d ⋅ a = da, however ba ≠ d

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 = ababa
2. d = acb
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.	a²d³a ⇒ da²	[15]
2.	a²d⁴ ⇒ dad	[16]
3.	a²d³c ⇒ dac	[13]
4.	ca ⇒ ad²a	[9]
5.	cd ⇒ ad³	[10]
6.	c² ⇒ ad²c	[12]
7.	acb ⇒ d	[3]
8.	bd ⇒ dcb	[14]
9.	ba² ⇒ da	[4]
10.	bad ⇒ d²	[6]
11.	abc ⇒ cba	[8]
12.	bac ⇒ dc	[11]
13.	a(ba)² ⇒ c	[2]

# ab:aabababa=baa reversed:ad/c/b ababa=c,acb=d morph:5/1,3/0
aaddda=daa
aadddd=dad
aadddc=dac
ca=adda
cd=addd
cc=addc
acb=d
bd=dcb
baa=da
bad=dd
abc=cba
bac=dc
ababa=c