⟨a, b | abaaba=abbab⟩

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

#	Rule	Proof
1.	abc ⇒ cba	[4]
2.	c²acbc ⇒ c²bc²a	[11]
3.	c(ca)² ⇒ c²bc	[9]
4.	c²bcb²c ⇒ c²ac³a	[14]
5.	c(cb)³ ⇒ (c²a)²c	[22]
6.	c(cb)²a ⇒ c²ac²	[12]
7.	cbacbc ⇒ cb²c²a	[10]
8.	c²bab ⇒ c²ac	[7]
9.	cbaca ⇒ cb²c	[8]
10.	ab²c ⇒ c²a	[6]
11.	c²ac²b²c ⇒ c(cb)²c²a	[20]
12.	aba ⇒ c	[2]
13.	c²ac²ba ⇒ c²(bc)²	[13]
14.	c(b²c)² ⇒ cbac³a	[19]
15.	cb²(cb)² ⇒ cbac²ac	[23]
16.	cb²cba ⇒ cbac²	[17]
17.	cb²ab ⇒ cbac	[5]
18.	cbac²b²c ⇒ cb²cbc²a	[21]
19.	cbac²ba ⇒ cb(bc)²	[18]
20.	c²acbab ⇒ c²bc²	[16]
21.	(cba)²b ⇒ cb²c²	[15]
22.	ab²ab ⇒ c²	[3]

# ab:abaaba=abbab c/ba aba=c morph:3/0 abc=cba ccacbc=ccbcca ccaca=ccbc ccbcbbc=ccaccca ccbcbcb=ccaccac ccbcba=ccacc cbacbc=cbbcca ccbab=ccac cbaca=cbbc abbc=cca ccaccbbc=ccbcbcca aba=c ccaccba=ccbcbc cbbcbbc=cbaccca cbbcbcb=cbaccac cbbcba=cbacc cbbab=cbac cbaccbbc=cbbcbcca cbaccba=cbbcbc ccacbab=ccbcc cbacbab=cbbcc abbab=cc

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#5852 ⟨a, b | abaaba=abbab⟩

Contents

Properties

Rewriting system