#4769 ⟨a, b | abaaabab=aba⟩

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

#	Rule	Proof
1.	ca ⇒ cbc	[6]
2.	(cb)²a ⇒ c²bab	[7]
3.	aba ⇒ cbab	[3]
4.	cba³ ⇒ c²bab²c	[12]
5.	cbc²bab² ⇒ c	[9]
6.	cbab²a ⇒ abcbab	[5]
7.	c²bab³a ⇒ (cbab)²	[8]
8.	c²bab²cba ⇒ cba²cbab	[13]
9.	cba²cbab² ⇒ cba	[14]
10.	(c²bab²)² ⇒ cba²	[11]

# ab:abaaabab=aba reversed:c/ba abaaa=c morph:5/1
ca=cbc
cbcba=ccbab
aba=cbab
cbaaa=ccbabbc
cbccbabb=c
cbabba=abcbab
ccbabbba=cbabcbab
ccbabbcba=cbaacbab
cbaacbabb=cba
ccbabbccbabb=cbaa