#4097 ⟨a, b | aabaabbaa=ab⟩

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

#	Rule	Proof
1.	a²ba²c ⇒ ab	[3]
2.	caba²c ⇒ cb	[5]
3.	acba²(ca²)² ⇒ abc	[11]
4.	c²ba²(ca²)² ⇒ cbc	[14]
5.	b²a² ⇒ c	[2]
6.	ab²c ⇒ acb(a²c)²ba²	[12]
7.	cb²c ⇒ c²b(a²c)²ba²	[15]
8.	(a²b)²c ⇒ ac(ca²)²	[17]
9.	caba²bc ⇒ c²(ca²)²	[18]
10.	b²ac ⇒ (cba²)²	[8]
11.	(ab)²a²c ⇒ ab²	[6]
12.	cbaba²c ⇒ cb²	[7]
13.	abcba²c ⇒ acb(a²c)²ab	[13]
14.	(cb)²a²c ⇒ c²b(a²c)²ab	[16]
15.	ab³ ⇒ acb(a²c)²	[9]
16.	cb³ ⇒ c²b(a²c)²	[10]
17.	b²ab ⇒ cba²c	[4]
18.	(ab)²a²bc ⇒ abc(ca²)²	[19]
19.	cbaba²bc ⇒ cbc(ca²)²	[20]
20.	abcba²bc ⇒ acb(a²c)²ac(ca²)²	[21]
21.	(cb)²a²bc ⇒ c²b(a²c)²ac(ca²)²	[22]

# ab:aabaabbaa=ab reversed:a/c/b bbaa=c morph:4/0
aabaac=ab
cabaac=cb
acbaacaacaa=abc
ccbaacaacaa=cbc
bbaa=c
abbc=acbaacaacbaa
cbbc=ccbaacaacbaa
aabaabc=accaacaa
cabaabc=cccaacaa
bbac=cbaacbaa
ababaac=abb
cbabaac=cbb
abcbaac=acbaacaacab
cbcbaac=ccbaacaacab
abbb=acbaacaac
cbbb=ccbaacaac
bbab=cbaac
ababaabc=abccaacaa
cbabaabc=cbccaacaa
abcbaabc=acbaacaacaccaacaa
cbcbaabc=ccbaacaacaccaacaa