⟨a, b | aabbbba=baa⟩

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

#	Rule	Proof
1.	a²e⁴ ⇒ ea	[13]
2.	a²e³d ⇒ e	[8]
3.	da ⇒ e	[4]
4.	de ⇒ eae³d	[10]
5.	ca ⇒ a²d	[7]
6.	ce ⇒ ead	[9]
7.	ba² ⇒ a²c	[5]
8.	bea ⇒ a²ea(eae³)³d	[15]
9.	baea ⇒ a⁴(eae³)⁴d	[16]
10.	be² ⇒ a(ae)²(ae⁴)³e³d	[29]
11.	bae² ⇒ a⁴e(ae⁴)⁴e³d	[35]
12.	a(ae)³e³ae³d² ⇒ be	[11]
13.	a⁴(eae³)³d² ⇒ bae	[12]
14.	a²e³cd ⇒ ec	[14]
15.	dc ⇒ cd	[6]
16.	dbe ⇒ (ea)³e⁴ae³d²	[25]
17.	dbae ⇒ ea³(eae³)³d²	[31]
18.	cbe ⇒ a²e²a(eae³)²d²	[28]
19.	cbae ⇒ a²ea²(eae³)³d²	[34]
20.	b²e ⇒ a(ae)²(eae³)²d²	[26]
21.	babe ⇒ a⁴(eae⁴)²ae³d²	[27]
22.	(be)² ⇒ a(ae)²(ae⁴)³ea(eae³)²d²	[30]
23.	baebe ⇒ a⁴e(ae⁴)⁴ea(eae³)²d²	[36]
24.	b²ae ⇒ a⁴e(eae³)³d²	[32]
25.	(ba)²e ⇒ a⁴ea(eae³)³d²	[33]
26.	bebae ⇒ a(ae)²(ae⁴)³a²(eae³)³d²	[37]
27.	(bae)² ⇒ a⁴e(ae⁴)⁴a²(eae³)³d²	[38]
28.	a(ae)³e³ae³cd² ⇒ bec	[17]
29.	a⁴(eae³)³cd² ⇒ baec	[18]
30.	a²e³c²d ⇒ ec²	[19]
31.	a(ae)³e³ae³c²d² ⇒ bec²	[20]
32.	a⁴(eae³)³c²d² ⇒ baec²	[21]
33.	a²e³c³d ⇒ ec³	[22]
34.	c⁴ ⇒ d	[3]
35.	b⁴a ⇒ c	[2]
36.	a(ae)³e³ae³c³d² ⇒ bec³	[23]
37.	a⁴(eae³)³c³d² ⇒ baec³	[24]

# ab:aabbbba=baa reversed:a/e/dcb bbbba=c,cccc=d,da=e morph:5/2,4/0,2/0 aaeeee=ea aaeeed=e da=e de=eaeeed ca=aad ce=ead baa=aac bea=aaeaeaeeeeaeeeeaeeed baea=aaaaeaeeeeaeeeeaeeeeaeeed bee=aaeaeaeeeeaeeeeaeeeeeeed baee=aaaaeaeeeeaeeeeaeeeeaeeeeeeed aaeaeaeeeeaeeedd=be aaaaeaeeeeaeeeeaeeedd=bae aaeeecd=ec dc=cd dbe=eaeaeaeeeeaeeedd dbae=eaaaeaeeeeaeeeeaeeedd cbe=aaeeaeaeeeeaeeedd cbae=aaeaaeaeeeeaeeeeaeeedd bbe=aaeaeeaeeeeaeeedd babe=aaaaeaeeeeeaeeeeaeeedd bebe=aaeaeaeeeeaeeeeaeeeeeaeaeeeeaeeedd baebe=aaaaeaeeeeaeeeeaeeeeaeeeeeaeaeeeeaeeedd bbae=aaaaeeaeeeeaeeeeaeeedd babae=aaaaeaeaeeeeaeeeeaeeedd bebae=aaeaeaeeeeaeeeeaeeeeaaeaeeeeaeeeeaeeedd baebae=aaaaeaeeeeaeeeeaeeeeaeeeeaaeaeeeeaeeeeaeeedd aaeaeaeeeeaeeecdd=bec aaaaeaeeeeaeeeeaeeecdd=baec aaeeeccd=ecc aaeaeaeeeeaeeeccdd=becc aaaaeaeeeeaeeeeaeeeccdd=baecc aaeeecccd=eccc cccc=d bbbba=c aaeaeaeeeeaeeecccdd=beccc aaaaeaeeeeaeeeeaeeecccdd=baeccc

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#2287 ⟨a, b | aabbbba=baa⟩

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