⟨a, b | aabbaa=aaab⟩

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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 = aaab
Reduction order:
- Left-to-right shortlex with b < c < a
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	cba² ⇒ ac	[7]
2.	acab ⇒ cbc	[8]
3.	a³b ⇒ c	[2]
4.	cb²a² ⇒ cab	[5]
5.	c(ab)² ⇒ cb²c	[12]
6.	acb²c ⇒ cbcab	[15]
7.	aca²b ⇒ cbac	[9]
8.	a²b²c ⇒ cab	[19]
9.	cbacbc ⇒ ac²ab	[10]
10.	cab³c ⇒ cb²cab	[21]
11.	cab²a² ⇒ ca²b	[20]
12.	caba²b ⇒ cb²ac	[13]
13.	ca(ab)² ⇒ cab²c	[23]
14.	acb²ac ⇒ cbca²b	[28]
15.	a²b²ac ⇒ ca²b	[6]
16.	a²b²a² ⇒ c	[3]
17.	cb²acbc ⇒ (cab)²	[14]
18.	c(bac)² ⇒ ac²a²b	[17]
19.	cab³ac ⇒ cb²ca²b	[29]
20.	cab³a² ⇒ cb²c	[11]
21.	ca²b³c ⇒ cab²cab	[25]
22.	c(a²b)² ⇒ cab²ac	[24]
23.	cb(bac)² ⇒ cabca²b	[16]
24.	cab²acbc ⇒ ca²bcab	[26]
25.	ca²b³ac ⇒ cab²ca²b	[30]
26.	ca²b³a² ⇒ cab²c	[22]
27.	cab(bac)² ⇒ (ca²b)²	[27]

# ab:aabbaa=aaab bca aaab=c magic:0 cbaa=ac acab=cbc aaab=c cbbaa=cab cabab=cbbc acbbc=cbcab acaab=cbac aabbc=cab cbacbc=accab cabbbc=cbbcab cabbaa=caab cabaab=cbbac caabab=cabbc acbbac=cbcaab aabbac=caab aabbaa=c cbbacbc=cabcab cbacbac=accaab cabbbac=cbbcaab cabbbaa=cbbc caabbbc=cabbcab caabaab=cabbac cbbacbac=cabcaab cabbacbc=caabcab caabbbac=cabbcaab caabbbaa=cabbc cabbacbac=caabcaab

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#2522 ⟨a, b | aabbaa=aaab⟩

Contents

Properties

Rewriting system