#4340 ⟨a, b | abbabaaab=aa⟩

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

#	Rule	Proof
1.	dcac ⇒ c²ad	[5]
2.	c²ac ⇒ d	[3]
3.	d²a²c ⇒ da²	[15]
4.	cda²c ⇒ ca²	[14]
5.	da²b ⇒ c²a²	[7]
6.	dca²b ⇒ da	[9]
7.	c²a²b ⇒ ca	[6]
8.	da³c ⇒ d³a²d	[24]
9.	ca³c ⇒ cd²a²d	[23]
10.	ada²c ⇒ a³	[13]
11.	d³a²dac ⇒ dada²d	[27]
12.	cd²a²dac ⇒ cada²d	[26]
13.	da(ac)² ⇒ d²a²d	[16]
14.	ca(ac)² ⇒ cda²d	[18]
15.	aca²b ⇒ a²	[4]
16.	ca²ba ⇒ da²c	[12]
17.	da²cba ⇒ caca²c	[29]
18.	a⁴c ⇒ ad²a²d	[22]
19.	ad²a²dac ⇒ (a²d)²	[25]
20.	a³cac ⇒ ada²d	[20]
21.	da⁴b ⇒ d²a³	[17]
22.	ca⁴b ⇒ cda³	[19]
23.	b(ba)² ⇒ c	[2]
24.	da(ba)² ⇒ dca²c	[11]
25.	ca(ba)² ⇒ c²a²c	[10]
26.	a³ba ⇒ (ac)²a²c	[28]
27.	daca²cba ⇒ c²(a²c)²	[31]
28.	a⁵b ⇒ ada³	[21]
29.	a²(ba)² ⇒ aca²c	[8]
30.	(ac)²a²cba ⇒ (a²c)²	[30]

# ab:abbabaaab=aa reversed:dc/ba bbaba=c,ccac=d morph:5/3,4/2
dcac=ccad
ccac=d
ddaac=daa
cdaac=caa
daab=ccaa
dcaab=da
ccaab=ca
daaac=dddaad
caaac=cddaad
adaac=aaa
dddaadac=dadaad
cddaadac=cadaad
daacac=ddaad
caacac=cdaad
acaab=aa
caaba=daac
daacba=cacaac
aaaac=addaad
addaadac=aadaad
aaacac=adaad
daaaab=ddaaa
caaaab=cdaaa
bbaba=c
dababa=dcaac
cababa=ccaac
aaaba=acacaac
dacaacba=ccaacaac
aaaaab=adaaa
aababa=acaac
acacaacba=aacaac