#4566 ⟨a, b | aaabbbaa=aab⟩

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:
- Left-to-right recursive path with deg(a) = deg(c) = 0, a < c; deg(b) = 1
Auxiliary generators:
1. bbbaa=c
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	(ca)⁴a ⇒ c²	[7]
2.	c²(ca)³a ⇒ c(ac)⁴	[10]
3.	a³(ca)³a ⇒ a²c	[6]
4.	a²c(ca)³a ⇒ a²(ac)⁴	[9]
5.	ca(ac)³a² ⇒ cac	[8]
6.	cac(ca)³a ⇒ ca(ac)⁴	[11]
7.	cb ⇒ cac	[4]
8.	a²b ⇒ a³c	[3]
9.	cab ⇒ ca²c	[5]
10.	b³a² ⇒ c	[2]

# ab:aaabbbaa=aab ac/b bbbaa=c morph:5/0
cacacacaa=cc
cccacacaa=cacacacac
aaacacacaa=aac
aaccacacaa=aaacacacac
caacacacaa=cac
caccacacaa=caacacacac
cb=cac
aab=aaac
cab=caac
bbbaa=c