#3787 ⟨a, b | ababbbaaab=a⟩

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(c) = 0, a < c; deg(b) = 1
Auxiliary generators:
1. abbb=c
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	a⁴ca²c ⇒ a³c²a³	[17]
2.	(aca²)²c ⇒ aca²c²a³	[12]
3.	a³c²a(a²c)² ⇒ aca²c²a³ca²	[14]
4.	aca²c²a(a²c)² ⇒ a	[10]
5.	ab ⇒ aca²c	[9]
6.	a³cb ⇒ a³c²a²c	[16]
7.	aca²cb ⇒ a(ca²c)²	[11]
8.	a³c²a²cb ⇒ aca²c²a³cac	[15]
9.	a(ca²c)²b ⇒ c	[13]

# ab:ababbbaaab=a reversed:ac/b abbb=c morph:4/2
aaaacaac=aaaccaaa
acaaacaac=acaaccaaa
aaaccaaacaac=acaaccaaacaa
acaaccaaacaac=a
ab=acaac
aaacb=aaaccaac
acaacb=acaaccaac
aaaccaacb=acaaccaaacac
acaaccaacb=c