#5228 ⟨a, b | aabbaba=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 recursive path with deg(a) = deg(c) = 0, a < c; deg(b) = 1
Auxiliary generators:
1. abba=c
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	ac²ba² ⇒ abc	[6]
2.	c³ba² ⇒ cbc	[8]
3.	ab²a ⇒ c	[2]
4.	(ab)² ⇒ acba	[3]
5.	cb²a ⇒ ab²c	[4]
6.	cbab ⇒ c²ba	[5]
7.	acba²b ⇒ abacba	[7]
8.	a(cba)² ⇒ abcb	[10]
9.	c²ba²b ⇒ (cba)²	[9]
10.	c(cba)² ⇒ (cb)²	[11]
11.	abcb² ⇒ acbac²ba	[12]
12.	ab(cb)²a ⇒ ac²bacb	[14]
13.	abcbc²ba² ⇒ a(cbac)²	[13]
14.	cbcb² ⇒ (c²ba)²	[15]
15.	(cb)³a ⇒ c³bacb	[17]
16.	(cb)²c²ba² ⇒ (c²ba)²c	[16]
17.	(acb)²b ⇒ a(bac)²cba	[18]
18.	(acb)²cba ⇒ abac²bacb	[20]
19.	(acb)²c²ba² ⇒ aba(cbac)²	[22]
20.	c²bacb² ⇒ (cba)²c²ba	[19]
21.	c²ba(cb)²a ⇒ (cbac)²b	[21]
22.	c²bacbc²ba² ⇒ cba(cbac)²	[23]

# ab:aabbaba=abab ac/b abba=c morph:4/4
accbaa=abc
cccbaa=cbc
abba=c
abab=acba
cbba=abbc
cbab=ccba
acbaab=abacba
acbacba=abcb
ccbaab=cbacba
ccbacba=cbcb
abcbb=acbaccba
abcbcba=accbacb
abcbccbaa=acbaccbac
cbcbb=ccbaccba
cbcbcba=cccbacb
cbcbccbaa=ccbaccbac
acbacbb=abacbaccba
acbacbcba=abaccbacb
acbacbccbaa=abacbaccbac
ccbacbb=cbacbaccba
ccbacbcba=cbaccbacb
ccbacbccbaa=cbacbaccbac