#21749 ⟨a, b | aaa=1, abbbbba=b⟩

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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

Auxiliary generators:
1. c = bbb
2. d = acbacba
Reduction order:
- Left-to-right recursive path with deg(c) = deg(b) = deg(d) = 0, c < b < d; deg(a) = 1
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	bc ⇒ cb	[6]
2.	dc ⇒ cd	[26]
3.	db ⇒ bd	[61]
4.	c²d ⇒ b²	[20]
5.	b³ ⇒ c	[3]
6.	c²bd ⇒ c	[21]
7.	cb²d ⇒ b	[56]
8.	cbd² ⇒ d	[73]
9.	cacbd ⇒ ca	[43]
10.	bacbd ⇒ ba	[44]
11.	dacbd ⇒ da	[70]
12.	c²a ⇒ ac²	[9]
13.	b²a ⇒ dac²	[24]
14.	bda ⇒ cab²d²	[62]
15.	d²a ⇒ cbad³	[76]
16.	c²ba ⇒ bac²	[10]
17.	a²c ⇒ cdac²b²	[38]
18.	a²b ⇒ cdac²	[37]
19.	a²d ⇒ cdab	[69]
20.	acba ⇒ bacd²	[68]
21.	acda ⇒ cd²	[67]
22.	ca² ⇒ dac³b²	[39]
23.	ba² ⇒ acb²	[8]
24.	(ba)² ⇒ acac³b²	[81]
25.	da² ⇒ bacd	[71]
26.	daca ⇒ cabacd⁵	[84]
27.	daba ⇒ b(ac)²b²	[82]
28.	a³ ⇒ 1	[1]
29.	a(ca)² ⇒ badabd³	[77]

# ab:aaa=1,abbbbba=b cbd/a bbb=c,acbacba=d morph:3/0,7/0
bc=cb
dc=cd
db=bd
ccd=bb
bbb=c
ccbd=c
cbbd=b
cbdd=d
cacbd=ca
bacbd=ba
dacbd=da
cca=acc
bba=dacc
bda=cabbdd
dda=cbaddd
ccba=bacc
aac=cdaccbb
aab=cdacc
aad=cdab
acba=bacdd
acda=cdd
caa=dacccbb
baa=acbb
baba=acacccbb
daa=bacd
daca=cabacddddd
daba=bacacbb
aaa=1
acaca=badabddd