⟨a, b | aaabba=abaab⟩

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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 = aba
Reduction order:
- Right-to-left recursive path with deg(a) = 0; deg(c) = deg(b) = 1, c < b
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	aba ⇒ c	[2]
2.	cba ⇒ abc	[4]
3.	a³b²a ⇒ cab	[3]
4.	cab²a ⇒ a³b²c	[6]
5.	ca²b²a ⇒ abcab	[7]
6.	ca³b²ca ⇒ a³b²c²	[11]
7.	a³b²cab ⇒ ca³b²c	[8]
8.	a³b²c²b ⇒ c²a³b²c	[12]
9.	ca²b²cab ⇒ abca³b²c	[10]
10.	ca²b²c²b ⇒ abc²a³b²c	[15]
11.	c²ab²cab ⇒ (a³b²c)²	[9]
12.	a³b²c²a²b²ca ⇒ c³ab²c²	[13]
13.	c²ab²c²b ⇒ a³b²c²a³b²c	[14]
14.	(ca²b²c)²a ⇒ abc³ab²c²	[17]
15.	c²ab²c²a²b²ca ⇒ a³b²c³ab²c²	[16]

# ab:aaabba=abaab reversed:a/cb aba=c morph:3/0 aba=c cba=abc aaabba=cab cabba=aaabbc caabba=abcab caaabbca=aaabbcc aaabbcab=caaabbc aaabbccb=ccaaabbc caabbcab=abcaaabbc caabbccb=abccaaabbc ccabbcab=aaabbcaaabbc aaabbccaabbca=cccabbcc ccabbccb=aaabbccaaabbc caabbccaabbca=abcccabbcc ccabbccaabbca=aaabbcccabbcc

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#5606 ⟨a, b | aaabba=abaab⟩

Contents

Properties

Rewriting system