⟨a, b | abaaaab=aaba⟩

Format:	Pretty Plain
Word to reduce:
	Tips: Lowercase letters stand for generators. Spaces are ignored. Numbers repeat the previous letter, e.g. `b90`.
Reduction strategy:	Leftmost Rightmost
Path to normal form:	1 1

Reduction order:
- Left-to-right shortlex with c < a < b < d < e
Auxiliary generators:
1. ba=c
2. caa=d
3. ada=e
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	ba ⇒ c	[2]
2.	ed ⇒ ae	[20]
3.	ca² ⇒ d	[3]
4.	cda ⇒ be	[7]
5.	cea ⇒ cde	[24]
6.	ceb ⇒ dc	[11]
7.	a²c ⇒ eb	[6]
8.	ada ⇒ e	[4]
9.	aea ⇒ ade	[21]
10.	beb ⇒ cac	[10]
11.	dca ⇒ cec	[17]
12.	d²a ⇒ cae	[8]
13.	dea ⇒ d²e	[25]
14.	eca ⇒ a²d	[14]
15.	e²a ⇒ ae²	[26]
16.	(ca)² ⇒ bec	[18]
17.	caeb ⇒ dac	[12]
18.	ce²c ⇒ c²e²	[62]
19.	ce²b ⇒ cbe²	[59]
20.	adeb ⇒ eac	[13]
21.	ae²c ⇒ ace²	[64]
22.	ae²b ⇒ abe²	[58]
23.	beac ⇒ cdeb	[16]
24.	daca ⇒ caec	[35]
25.	d²ec ⇒ be²	[51]
26.	d²eb ⇒ bead	[47]
27.	de²c ⇒ dce²	[65]
28.	de²b ⇒ dbe²	[60]
29.	(ec)² ⇒ a³d	[23]
30.	eaca ⇒ adec	[36]
31.	ebda ⇒ a²be	[15]
32.	ebea ⇒ ebde	[28]
33.	e³c ⇒ ece²	[56]
34.	e³b ⇒ ebe²	[52]
35.	c²aec ⇒ cad	[44]
36.	cadec ⇒ bead	[57]
37.	cec²a ⇒ dbec	[33]
38.	acaec ⇒ a²d	[43]
39.	a²bec ⇒ ec²a	[32]
40.	a²dec ⇒ ead	[45]
41.	bec²a ⇒ cabec	[34]
42.	dadec ⇒ ce²	[48]
43.	eadec ⇒ acae²	[49]
44.	ebdec ⇒ ecdeb	[55]
45.	ebe²c ⇒ ebce²	[63]
46.	ebe²b ⇒ eb²e²	[53]
47.	caec²a ⇒ dabec	[46]
48.	cecdec ⇒ dbead	[67]
49.	cecdeb ⇒ dcdec	[38]
50.	a²bead ⇒ ecdec	[61]
51.	adec²a ⇒ eabec	[50]
52.	becdec ⇒ cabead	[68]
53.	becdeb ⇒ cacdec	[39]
54.	beabec ⇒ cdec²a	[42]
55.	ebcaec ⇒ ecd	[54]
56.	caecdec ⇒ dabead	[69]
57.	caecdeb ⇒ dacdec	[40]
58.	a(dec)² ⇒ eabead	[70]
59.	adecdeb ⇒ eacdec	[41]
60.	(bea)²d ⇒ c(dec)²	[66]
61.	ecdebec ⇒ a²bea²d	[71]
62.	ebdebec ⇒ ecdec²a	[72]
63.	ec(dec)² ⇒ a(abe)²e	[73]

Up:	Monoids with two generators and one relation
Prev:	#5282 ⟨a, b \| abaaaab=aaab⟩
Next:	#5284 ⟨a, b \| abaaaab=aabb⟩

#5283 ⟨a, b | abaaaab=aaba⟩

Quick links

Properties

Rewriting system