#4780 ⟨a, b | abaaabba=bab⟩

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

#	Rule	Proof
1.	ab ⇒ c	[2]
2.	aca²cbc ⇒ c²b	[6]
3.	ca²cba ⇒ bc	[4]
4.	c²b² ⇒ a(ca²c)²bc	[9]
5.	bcb ⇒ ca²cbc	[5]
6.	c²bca²cbc ⇒ a(ca²c)²bc²b	[10]
7.	bc²a²cbc ⇒ ca²cbc²b	[7]
8.	c²ba²cba ⇒ aca²cb²c	[8]

# ab:abaaabba=bab reversed:ca/b ab=c morph:2/0
ab=c
acaacbc=ccb
caacba=bc
ccbb=acaaccaacbc
bcb=caacbc
ccbcaacbc=acaaccaacbccb
bccaacbc=caacbccb
ccbaacba=acaacbbc