#5313 ⟨a, b | abaabab=abba⟩

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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. abba=c
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	ab²a ⇒ c	[2]
2.	cb²a ⇒ ab²c	[4]
3.	c(ba)² ⇒ ca²bc	[8]
4.	aba²bc ⇒ cba	[6]
5.	ca(ab)² ⇒ cba	[13]
6.	cba²bc ⇒ ab²cba	[9]
7.	(aba)²b ⇒ c	[3]
8.	cba³bc ⇒ ca²bcba	[10]
9.	cba(ab)² ⇒ ab²c	[7]
10.	ca(abc)² ⇒ (cb)²a	[12]
11.	cba³bab ⇒ ca²bc	[14]
12.	ca²bc(ab)² ⇒ cbc	[11]

# ab:abaabab=abba abc abba=c magic:0
abba=c
cbba=abbc
cbaba=caabc
abaabc=cba
caabab=cba
cbaabc=abbcba
abaabab=c
cbaaabc=caabcba
cbaabab=abbc
caabcabc=cbcba
cbaaabab=caabc
caabcabab=cbc