⟨a, b | aababbba=ab⟩

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#1977 ⟨a, b | aababbba=aa⟩

#1979 ⟨a, b | aababbba=ba⟩

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

#	Rule	Proof
1.	ab³ ⇒ c	[2]
2.	a²bca ⇒ ab	[3]
3.	a²bc² ⇒ cb	[4]
4.	ab²ca ⇒ a²bcb	[10]
5.	cabca ⇒ cb	[9]
6.	cb⁴ ⇒ cabc²	[13]
7.	cb²ca ⇒ cabcb	[16]
8.	(ab)²ca ⇒ ab²	[5]
9.	(ab)²cb ⇒ c²a	[12]
10.	(ab)²c² ⇒ cb²	[6]
11.	cbabca ⇒ cb²	[11]
12.	cbabc² ⇒ cabc²b	[14]
13.	cb³ca ⇒ cbabcb	[19]
14.	ab²abca ⇒ c	[7]
15.	ab²abcb ⇒ cbca	[17]
16.	ab²abc² ⇒ cb³	[8]
17.	cb²abca ⇒ cb³	[15]
18.	cb²abcb ⇒ cabc³a	[20]
19.	cb²abc² ⇒ cabc²b²	[21]
20.	cb³abca ⇒ cabc²	[18]
21.	cb³abcb ⇒ cabc²bca	[23]
22.	cb³abc² ⇒ cabc²b³	[22]

# ab:aababbba=ab abc abbb=c morph:4/0 abbb=c aabca=ab aabcc=cb abbca=aabcb cabca=cb cbbbb=cabcc cbbca=cabcb ababca=abb ababcb=cca ababcc=cbb cbabca=cbb cbabcc=cabccb cbbbca=cbabcb abbabca=c abbabcb=cbca abbabcc=cbbb cbbabca=cbbb cbbabcb=cabccca cbbabcc=cabccbb cbbbabca=cabcc cbbbabcb=cabccbca cbbbabcc=cabccbbb

#1978 ⟨a, b | aababbba=ab⟩

Contents

Properties

Rewriting system

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