#5390 ⟨a, b | abbaaab=baab⟩

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

#	Rule	Proof
1.	ba²b ⇒ c	[2]
2.	ba²c ⇒ ca²b	[4]
3.	(ba)²c ⇒ c²a²b	[8]
4.	abcac ⇒ c²a²b	[14]
5.	cba³b ⇒ bac	[7]
6.	abca²b ⇒ bac	[13]
7.	cba³c ⇒ baca²b	[9]
8.	abca²c ⇒ baca²b	[15]
9.	bac²ac ⇒ c²abac	[11]
10.	ab²a³b ⇒ c	[3]
11.	bac²a²b ⇒ c²ac	[10]
12.	ab²a³c ⇒ ca²b	[6]
13.	bac²a²c ⇒ c²aca²b	[12]
14.	abcabac ⇒ c²ac	[16]
15.	bac²abac ⇒ (c²a)²ab	[17]

# ab:abbaaab=baab reversed:abc baab=c magic:0
baab=c
baac=caab
babac=ccaab
abcac=ccaab
cbaaab=bac
abcaab=bac
cbaaac=bacaab
abcaac=bacaab
baccac=ccabac
abbaaab=c
baccaab=ccac
abbaaac=caab
baccaac=ccacaab
abcabac=ccac
baccabac=ccaccaab