#4156 ⟨a, b | aabbaaaba=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:
- Left-to-right recursive path with deg(a) = deg(c) = 0, a < c; deg(b) = 1
Auxiliary generators:
1. abb=c
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	aca³ba ⇒ ab	[3]
2.	aca³bc ⇒ cb	[4]
3.	c²a³ba ⇒ cb	[7]
4.	ab² ⇒ c	[2]
5.	abca³ba ⇒ c	[5]
6.	cb² ⇒ abca³bc	[6]
7.	cba³ba ⇒ aca²c	[8]
8.	cbca³ba ⇒ abca³bc	[10]
9.	c²a³bcb ⇒ cbca³bc	[11]
10.	abca³bcb ⇒ c²a³bc	[9]
11.	cba³bcb ⇒ aca²c²a³bc	[12]
12.	cbca³bcb ⇒ ab(ca³bc)²	[13]

# ab:aabbaaaba=ab ac/b abb=c morph:3/0
acaaaba=ab
acaaabc=cb
ccaaaba=cb
abb=c
abcaaaba=c
cbb=abcaaabc
cbaaaba=acaac
cbcaaaba=abcaaabc
ccaaabcb=cbcaaabc
abcaaabcb=ccaaabc
cbaaabcb=acaaccaaabc
cbcaaabcb=abcaaabccaaabc