⟨a, b | abaaab=aaaba⟩

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Monoids with two generators and one relation

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

Auxiliary generators:
1. c = ab
2. d = cc
3. e = aa
4. f = ec
5. g = de
Reduction order:
- Left-to-right recursive path with deg(d) = deg(f) = deg(g) = 0, d < f < g; deg(e) = 1; deg(c) = 2; deg(a) = 3; deg(b) = 4
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	gd ⇒ f²	[16]
2.	fdf ⇒ g²	[17]
3.	gf³ ⇒ fdg²	[22]
4.	de ⇒ g	[6]
5.	fe ⇒ df	[15]
6.	g²e ⇒ fd²f	[21]
7.	dc ⇒ cd	[10]
8.	fc ⇒ ed	[11]
9.	gc ⇒ df	[9]
10.	ec ⇒ f	[5]
11.	c² ⇒ d	[3]
12.	fa ⇒ cf	[8]
13.	ga ⇒ dae	[18]
14.	ea ⇒ ae	[12]
15.	a² ⇒ e	[4]
16.	gb ⇒ dac	[19]
17.	dfb ⇒ ced	[20]
18.	f²b ⇒ e²d	[23]
19.	g²fb ⇒ fged	[24]
20.	eb ⇒ ac	[13]
21.	cfb ⇒ ed	[14]
22.	ab ⇒ c	[2]

# ab:abaaab=aaaba dfg/e/c/a/b ab=c,cc=d,aa=e,ec=f,de=g morph:2/1,2/0,2/0,2/0,2/1 gd=ff fdf=gg gfff=fdgg de=g fe=df gge=fddf dc=cd fc=ed gc=df ec=f cc=d fa=cf ga=dae ea=ae aa=e gb=dac dfb=ced ffb=eed ggfb=fged eb=ac cfb=ed ab=c

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#5811 ⟨a, b | abaaab=aaaba⟩

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