#5349 ⟨a, b | ababaab=baba⟩

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(d) = 0; deg(b) = deg(c) = 1, b < c; deg(a) = 2
Auxiliary generators:
1. abab=c
2. aab=d
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	bc ⇒ cdb	[8]
2.	dc² ⇒ cd²b	[11]
3.	dabd ⇒ ca	[7]
4.	babd ⇒ cdab	[9]
5.	dcabd ⇒ cd²ab	[12]
6.	ac ⇒ dab	[6]
7.	(ba)² ⇒ cd	[4]
8.	dcaba ⇒ cd²	[10]
9.	a²b ⇒ d	[3]
10.	(ab)² ⇒ c	[2]

# ab:ababaab=baba reversed:d/bc/a abab=c,aab=d morph:4/1,3/0
bc=cdb
dcc=cddb
dabd=ca
babd=cdab
dcabd=cddab
ac=dab
baba=cd
dcaba=cdd
aab=d
abab=c