#5201 ⟨a, b | aababba=baba⟩

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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 shortlex with b < a < c
Auxiliary generators:
1. baba=c
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	bac ⇒ cba	[4]
2.	(ba)² ⇒ c	[2]
3.	a(ab)²c ⇒ cba	[6]
4.	c(ab)²c ⇒ babcba	[8]
5.	a²bab²a ⇒ c	[3]
6.	cabab²a ⇒ babc	[7]
7.	a²bab²c ⇒ babc	[10]
8.	(bab)²c ⇒ cabab²c	[9]
9.	a²cabab²c ⇒ cbc	[13]
10.	(ca)²bab²c ⇒ ba(bc)²	[14]
11.	a²bab³abc ⇒ cabab²c	[11]
12.	cabab³abc ⇒ babcabab²c	[12]

# ab:aababba=baba reversed:bac baba=c magic:0
bac=cba
baba=c
aababc=cba
cababc=babcba
aababba=c
cababba=babc
aababbc=babc
babbabc=cababbc
aacababbc=cbc
cacababbc=babcbc
aababbbabc=cababbc
cababbbabc=babcababbc