#4637 ⟨a, b | aababaab=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:
- Left-to-right recursive path with deg(c) = deg(b) = 0, c < b; deg(a) = 1
Auxiliary generators:
1. ababa=c
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	c⁹b ⇒ cbc	[18]
2.	ac⁸b ⇒ abc	[16]
3.	ca ⇒ ac⁴	[19]
4.	cba ⇒ abc	[6]
5.	a²c⁴bc⁸b ⇒ a²c⁴b²c	[20]
6.	aba ⇒ a²c⁴b	[21]
7.	a³c⁴bc⁶b ⇒ c	[23]
8.	a²c⁴b²a ⇒ c	[22]

# ab:aababaab=aba cb/a ababa=c morph:5/0
cccccccccb=cbc
accccccccb=abc
ca=acccc
cba=abc
aaccccbccccccccb=aaccccbbc
aba=aaccccb
aaaccccbccccccb=c
aaccccbba=c

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