⟨a, b | aaabba=baaa⟩

Up:

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 = bba
2. d = cc
3. e = dad
4. f = eaa
Reduction order:
- Right-to-left recursive path with deg(a) = 0; deg(f) = 1; deg(e) = 2; deg(d) = deg(c) = deg(b) = 3, d < c < b
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	a³f² ⇒ fa²	[24]
2.	a³fe ⇒ f	[15]
3.	ea² ⇒ f	[5]
4.	ef ⇒ fafe	[16]
5.	eaf ⇒ fa²fe	[17]
6.	da² ⇒ a³e	[13]
7.	df ⇒ a(a²f)²e²	[23]
8.	daf ⇒ fa²e	[14]
9.	dae ⇒ ead	[8]
10.	ca² ⇒ a³d	[12]
11.	cf ⇒ a³fa²e²	[21]
12.	caf ⇒ a⁶fafe²	[22]
13.	ba³ ⇒ a³c	[6]
14.	bf ⇒ a⁶fa²e³	[25]
15.	baf ⇒ a⁹fafe³	[26]
16.	ba²f ⇒ a⁹fa²fe³	[27]
17.	dad ⇒ e	[4]
18.	dc ⇒ cd	[7]
19.	dace ⇒ ecad	[11]
20.	c² ⇒ d	[3]
21.	b²a ⇒ c	[2]
22.	dacd ⇒ ec	[9]

# ab:aaabba=baaa reversed:a/f/e/dcb bba=c,cc=d,dad=e,eaa=f morph:3/2,2/1,3/2,3/0 aaaff=faa aaafe=f eaa=f ef=fafe eaf=faafe daa=aaae df=aaafaafee daf=faae dae=ead caa=aaad cf=aaafaaee caf=aaaaaafafee baaa=aaac bf=aaaaaafaaeee baf=aaaaaaaaafafeee baaf=aaaaaaaaafaafeee dad=e dc=cd dace=ecad cc=d bba=c dacd=ec

Up:	Monoid enumeration
Prev:	#2460 ⟨a, b \| aaabba=abbb⟩
Next:	#2462 ⟨a, b \| aaabba=baab⟩

#2461 ⟨a, b | aaabba=baaa⟩

Contents

Properties

Rewriting system