#4843 ⟨a, b | ababbaba=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:
- Left-to-right recursive path with deg(a) = 0; deg(c) = deg(b) = 1, c < b
Auxiliary generators:
1. bbaba=c
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	bc ⇒ c²a	[6]
2.	bab ⇒ abac	[3]
3.	abac² ⇒ bac²a	[8]
4.	aba(ca)² ⇒ c	[4]
5.	b²ac ⇒ cbaca	[10]
6.	ba²bac ⇒ abacab	[5]
7.	abacac² ⇒ cba(ca)²	[7]
8.	a(bac)² ⇒ (bac)²a	[12]
9.	a(baca)² ⇒ bac	[9]
10.	ab(ac)²bac ⇒ c(baca)²	[11]

# ab:ababbaba=bab a/cb bbaba=c morph:5/0
bc=cca
bab=abac
abacc=bacca
abacaca=c
bbac=cbaca
baabac=abacab
abacacc=cbacaca
abacbac=bacbaca
abacabaca=bac
abacacbac=cbacabaca