#5077 ⟨a, b | aaabbaa=baaa⟩

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

#	Rule	Proof
1.	a³dad² ⇒ dad	[25]
2.	a³dada² ⇒ da³	[28]
3.	a²(ad)³ ⇒ da²d	[30]
4.	a³(da)²c ⇒ da²c	[24]
5.	a³dcd ⇒ d²	[33]
6.	a³dadcd ⇒ dacd	[34]
7.	cad ⇒ ad²	[14]
8.	cd² ⇒ ada²dcd	[35]
9.	ca³ ⇒ ada²	[23]
10.	ca²d ⇒ (ad)²	[21]
11.	cdad ⇒ (ada)²d²	[27]
12.	cda³ ⇒ (ada)²da²	[29]
13.	cda²d ⇒ ada(ad)³	[31]
14.	a(ac)² ⇒ d	[3]
15.	ad(ac)² ⇒ cd	[13]
16.	ca²c ⇒ adac	[11]
17.	cda²c ⇒ (ada)²dac	[26]
18.	c²d ⇒ ad²(ac)²	[19]
19.	cacd ⇒ adcd	[32]
20.	(cd)² ⇒ (ada)²d²(ac)²	[37]
21.	cdacd ⇒ (ada)²dcd	[36]
22.	bd ⇒ dac	[10]
23.	bad ⇒ a²cd	[7]
24.	ba³ ⇒ a²ca²	[4]
25.	ba²d ⇒ a³d²	[20]
26.	ba²c ⇒ d	[6]
27.	bcd ⇒ a²cd(ac)²	[16]
28.	bacd ⇒ a³d²(ac)²	[22]
29.	ab² ⇒ c	[2]

# ab:aaabbaa=baaa reversed:ad/c/b abb=c,aacac=d morph:3/2,5/3
aaadadd=dad
aaadadaa=daaa
aaadadad=daad
aaadadac=daac
aaadcd=dd
aaadadcd=dacd
cad=add
cdd=adaadcd
caaa=adaa
caad=adad
cdad=adaadadd
cdaaa=adaadadaa
cdaad=adaadadad
aacac=d
adacac=cd
caac=adac
cdaac=adaadadac
ccd=addacac
cacd=adcd
cdcd=adaadaddacac
cdacd=adaadadcd
bd=dac
bad=aacd
baaa=aacaa
baad=aaadd
baac=d
bcd=aacdacac
bacd=aaaddacac
abb=c