#4192 ⟨a, b | aabbbaaab=ba⟩

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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(d) = deg(c) = 0, d < c; deg(a) = 1; deg(b) = 2
Auxiliary generators:
1. aab=c
2. bbbac=d
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	ca(ad)²c ⇒ a²d	[8]
2.	a⁴d ⇒ ca	[6]
3.	a(ad)³c ⇒ d	[11]
4.	(a²d)²adc ⇒ ca(ad)²a²d	[9]
5.	da((ad)²c)² ⇒ a(ad)³d	[16]
6.	a(ad)³a²d ⇒ da(ad)²c	[14]
7.	ca²((ad)²c)² ⇒ a²ca²dad²	[13]
8.	a²ca(ad)²a²d ⇒ ca³dadc	[10]
9.	a(ad)³da(ad)²c ⇒ da(ad)²c(ad)²a²d	[17]
10.	(a²(da)²)²d² ⇒ da²d(adc)²(ad)²c	[19]
11.	a²ca²dad²a(ad)²c ⇒ ca³dadc(ad)²a²d	[15]
12.	a²da²((ad)²c)² ⇒ ca(ad)²a²ca²dad²	[20]
13.	a(ad)³a²ca²dad² ⇒ da²((ad)²c)²	[21]
14.	a²ca²da²(ad)³d ⇒ ca³d(adc)²(ad)²c	[18]
15.	(a²ca(ad)²)²d ⇒ c²a²dc(ad)²c	[24]
16.	a(ad)³da²((ad)²c)² ⇒ da(ad)²c(ad)²a²ca²dad²	[23]
17.	a²ca²dad²a²((ad)²c)² ⇒ ca³dadc(ad)²a²ca²dad²	[22]
18.	a²b ⇒ c	[2]
19.	bd ⇒ a(ad)⁴c	[12]
20.	bc ⇒ a²dab	[7]
21.	ba ⇒ a²d	[5]

# ab:aabbbaaab=ba reversed:dc/a/b aab=c,bbbac=d morph:3/0,5/0
caadadc=aad
aaaad=ca
aadadadc=d
aadaadadc=caadadaad
daadadcadadc=aadadadd
aadadadaad=daadadc
caaadadcadadc=aacaadadd
aacaadadaad=caaadadc
aadadaddaadadc=daadadcadadaad
aadadaaadadadd=daadadcadcadadc
aacaadaddaadadc=caaadadcadadaad
aadaaadadcadadc=caadadaacaadadd
aadadadaacaadadd=daaadadcadadc
aacaadaaadadadd=caaadadcadcadadc
aacaadadaacaadadd=ccaadcadadc
aadadaddaaadadcadadc=daadadcadadaacaadadd
aacaadaddaaadadcadadc=caaadadcadadaacaadadd
aab=c
bd=aadadadadc
bc=aadab
ba=aad