#5270 ⟨a, b | aabbbba=abab⟩

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

#	Rule	Proof
1.	cab ⇒ abc	[4]
2.	(ab)² ⇒ c	[2]
3.	c²b³a ⇒ abcbab	[10]
4.	a²b⁴a ⇒ c	[3]
5.	a²b⁴c ⇒ cbab	[6]
6.	abcb³a ⇒ cbab	[8]
7.	c(bab)² ⇒ abcb³c	[7]
8.	cbcb³a ⇒ abcb³c	[9]
9.	c²b³cbab ⇒ a(bc)²b³c	[13]
10.	abcb³cbab ⇒ cbcb³c	[12]
11.	cbab²cb³a ⇒ cbcb³c	[16]
12.	cbcb³cbab ⇒ cbab²cb³c	[14]
13.	cba(b²cb)²ab ⇒ a(bcb³c)²	[15]

# ab:aabbbba=abab abc abab=c magic:0
cab=abc
abab=c
ccbbba=abcbab
aabbbba=c
aabbbbc=cbab
abcbbba=cbab
cbabbab=abcbbbc
cbcbbba=abcbbbc
ccbbbcbab=abcbcbbbc
abcbbbcbab=cbcbbbc
cbabbcbbba=cbcbbbc
cbcbbbcbab=cbabbcbbbc
cbabbcbbbcbab=abcbbbcbcbbbc