⟨a, b | ababaaaaab=a⟩

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

#	Rule	Proof
1.	dc ⇒ cecd	[16]
2.	de ⇒ ce³cd	[18]
3.	da ⇒ ad	[9]
4.	ca³c ⇒ e	[4]
5.	ca³e ⇒ ea³c	[6]
6.	ea⁴c ⇒ ca²c²d	[19]
7.	c²a⁴c ⇒ a	[14]
8.	eca⁴c ⇒ ca⁴	[10]
9.	ea⁴e ⇒ ca²ce²cd	[21]
10.	c²a⁴e ⇒ a⁴c	[15]
11.	eca⁴e ⇒ ca²cecd	[22]
12.	a⁵ ⇒ d	[3]
13.	aca⁴c ⇒ c²d	[17]
14.	aca⁴e ⇒ ce²cd	[20]
15.	db ⇒ a⁴c	[8]
16.	ab ⇒ c	[2]

# ab:ababaaaaab=a reversed:ce/da/b ab=c,aaaaa=d,caaac=e morph:2/2,5/0,5/4 dc=cecd de=ceeecd da=ad caaac=e caaae=eaaac eaaaac=caaccd ccaaaac=a ecaaaac=caaaa eaaaae=caaceecd ccaaaae=aaaac ecaaaae=caacecd aaaaa=d acaaaac=ccd acaaaae=ceecd db=aaaac ab=c

Up:	Monoid enumeration
Prev:	#3754 ⟨a, b \| abaabbbbba=b⟩
Next:	#3757 ⟨a, b \| ababaaabab=a⟩

#3755 ⟨a, b | ababaaaaab=a⟩

Contents

Properties

Rewriting system