⟨a, b, c | bb=ac, caa=a⟩

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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. d = aba
Reduction order:
- Right-to-left recursive path with deg(d) = deg(c) = 0, d < c; deg(b) = 1; deg(a) = 2
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	dc²dcd² ⇒ cdc²d³	[38]
2.	(c²d)²d ⇒ d	[36]
3.	dc²(dc)² ⇒ cdc²d²c	[44]
4.	bd² ⇒ cdcd²	[13]
5.	bdc ⇒ c(dc)²	[22]
6.	bcd² ⇒ cdc²d²	[25]
7.	bcdc ⇒ cdcb	[21]
8.	dc(cd)²b² ⇒ cdc²d²b²	[34]
9.	(c²d)²b² ⇒ b²	[39]
10.	b³ ⇒ cdc	[14]
11.	bdb² ⇒ (cd)²b²	[30]
12.	bcdb² ⇒ cdc²db²	[43]
13.	dc(cd)²a ⇒ cdc²d²a	[46]
14.	(c²d)²a ⇒ a	[35]
15.	bda ⇒ (cd)²a	[23]
16.	bcda ⇒ cdc²da	[31]
17.	ad ⇒ cdc²d²	[37]
18.	ac ⇒ b²	[1]
19.	abd ⇒ dba	[8]
20.	ab² ⇒ cdc²db²	[45]
21.	a² ⇒ cdc²da	[27]
22.	aba ⇒ d	[3]

# abc:bb=ac,caa=a reversed:dc/b/a aba=d morph:3/0 dccdcdd=cdccddd ccdccdd=d dccdcdc=cdccddc bdd=cdcdd bdc=cdcdc bcdd=cdccdd bcdc=cdcb dccdcdbb=cdccddbb ccdccdbb=bb bbb=cdc bdbb=cdcdbb bcdbb=cdccdbb dccdcda=cdccdda ccdccda=a bda=cdcda bcda=cdccda ad=cdccdd ac=bb abd=dba abb=cdccdbb aa=cdccda aba=d

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#3536 ⟨a, b, c | bb=ac, caa=a⟩

Contents

Properties

Rewriting system