⟨a, b | abaaab=aaba⟩

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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 = baa
2. d = aca
Reduction order:
- Left-to-right shortlex with a < b < c < d
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	dc ⇒ ad	[12]
2.	aca ⇒ d	[3]
3.	ada ⇒ acd	[13]
4.	ba² ⇒ c	[2]
5.	cba ⇒ bdb	[7]
6.	c²a ⇒ bad	[6]
7.	cda ⇒ c²d	[15]
8.	dba ⇒ a²c	[10]
9.	d²a ⇒ ad²	[16]
10.	a²ba ⇒ db	[4]
11.	ad²b ⇒ abd²	[18]
12.	caba ⇒ badb	[8]
13.	c²db ⇒ bdac	[27]
14.	cd²b ⇒ cbd²	[19]
15.	daba ⇒ acdb	[9]
16.	dbca ⇒ a²bd	[11]
17.	dbda ⇒ dbcd	[17]
18.	(db)² ⇒ a³c	[14]
19.	d³b ⇒ dbd²	[20]
20.	a²cdb ⇒ dac	[23]
21.	abadb ⇒ a²c	[22]
22.	cacdb ⇒ bd²	[24]
23.	dacdb ⇒ abad²	[25]
24.	dbd²b ⇒ db²d²	[21]
25.	db²adb ⇒ a²c²	[26]

# ab:abaaab=aaba abcd baa=c,aca=d morph:3/3,3/0 dc=ad aca=d ada=acd baa=c cba=bdb cca=bad cda=ccd dba=aac dda=add aaba=db addb=abdd caba=badb ccdb=bdac cddb=cbdd daba=acdb dbca=aabd dbda=dbcd dbdb=aaac dddb=dbdd aacdb=dac abadb=aac cacdb=bdd dacdb=abadd dbddb=dbbdd dbbadb=aacc

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#2565 ⟨a, b | abaaab=aaba⟩

Contents

Properties

Rewriting system