#4475 ⟨a, b | aaaabbba=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:
- a⁴b³ ⋅ a = ba² and ba ⋅ a = ba², however a⁴b³ ≠ 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 = bbb
2. d = caa
Reduction order:
- Right-to-left recursive path with deg(a) = deg(d) = 0, a < d; deg(c) = deg(b) = 1, c < b
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	a³(ad)³ ⇒ da	[11]
2.	a⁴(da)²ca ⇒ d	[6]
3.	cd ⇒ da²(da)²ca	[8]
4.	ca² ⇒ d	[3]
5.	cad ⇒ da³(da)²ca	[9]
6.	bd ⇒ da²ca	[7]
7.	ba² ⇒ a⁴ca	[4]
8.	bad ⇒ a⁴da²(da)²ca	[10]
9.	cb ⇒ bc	[5]
10.	b³ ⇒ c	[2]

# ab:aaaabbba=baa reversed:ad/cb bbb=c,caa=d morph:3/1,3/0
aaaadadad=da
aaaadadaca=d
cd=daadadaca
caa=d
cad=daaadadaca
bd=daaca
baa=aaaaca
bad=aaaadaadadaca
cb=bc
bbb=c