#5015 ⟨a, b | aaabaaa=abab⟩

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

#	Rule	Proof
1.	cbab ⇒ c²	[7]
2.	(ab)² ⇒ ac	[3]
3.	c²ab ⇒ cbac	[8]
4.	acab ⇒ abac	[4]
5.	cba³ ⇒ a²bac	[5]
6.	caba³ ⇒ a²ba²c	[6]
7.	a²ba³ ⇒ c	[2]
8.	cbaca³ ⇒ ca²ba²c	[11]
9.	abaca³ ⇒ a³ba²c	[10]
10.	c²aca³ ⇒ a²bacba²c	[12]
11.	(ac)²a³ ⇒ (aba²)²c	[13]

# ab:aaabaaa=abab reversed:b/ca aabaaa=c morph:6/0
cbab=cc
abab=ac
ccab=cbac
acab=abac
cbaaa=aabac
cabaaa=aabaac
aabaaa=c
cbacaaa=caabaac
abacaaa=aaabaac
ccacaaa=aabacbaac
acacaaa=abaaabaac