#5375 ⟨a, b | ababbba=baba⟩

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Properties
Rewriting system

Properties

Presentation has sum-of-sides 11
Infinite non-commutative monoid

Rewriting system

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

#	Rule	Proof
1.	ae²c ⇒ eae	[25]
2.	a(ec)² ⇒ cae	[27]
3.	aede ⇒ c	[16]
4.	ae²de ⇒ e²	[24]
5.	aecede ⇒ ce	[29]
6.	dc ⇒ cde	[18]
7.	dae ⇒ c	[6]
8.	de² ⇒ cede	[28]
9.	dac ⇒ aecde	[21]
10.	dec ⇒ cecde	[30]
11.	da²e ⇒ aec	[19]
12.	deae ⇒ cec	[26]
13.	ae²dba ⇒ eba	[20]
14.	aecedba ⇒ cba	[23]
15.	daba ⇒ aedba	[14]
16.	deba ⇒ cedba	[22]
17.	be ⇒ dadba	[11]
18.	bc ⇒ cdba	[17]
19.	bae ⇒ aedba	[15]
20.	bac ⇒ eba	[13]
21.	ba²e ⇒ aeba	[10]
22.	bd ⇒ db	[7]
23.	bade ⇒ edba	[12]
24.	b² ⇒ d	[3]
25.	(ba)² ⇒ ae	[5]
26.	badba ⇒ e	[4]

# ab:ababbba=baba reversed:aec/d/b bbbaba=c,bb=d,badba=e morph:6/1,2/1,5/0
aeec=eae
aecec=cae
aede=c
aeede=ee
aecede=ce
dc=cde
dae=c
dee=cede
dac=aecde
dec=cecde
daae=aec
deae=cec
aeedba=eba
aecedba=cba
daba=aedba
deba=cedba
be=dadba
bc=cdba
bae=aedba
bac=eba
baae=aeba
bd=db
bade=edba
bb=d
baba=ae
badba=e