#4042 ⟨a, b | aaabbbaba=ab⟩

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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. abbb=c
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	a²caba ⇒ ab	[3]
2.	a²cabc ⇒ cb	[4]
3.	(ca)²ba ⇒ cb	[11]
4.	abacaba ⇒ ab²	[5]
5.	cb² ⇒ abacabc	[6]
6.	cbacaba ⇒ abacabc	[12]
7.	c²(ab)² ⇒ ab²ac²	[21]
8.	a²cab² ⇒ abcaba	[7]
9.	(ca)²b² ⇒ cbcaba	[15]
10.	(ca)²bcb ⇒ cbacabc	[14]
11.	ab³ ⇒ c	[2]
12.	ab²acaba ⇒ c	[8]
13.	abc(ab)² ⇒ a²c²	[17]
14.	abacab² ⇒ ab²caba	[10]
15.	abacabcb ⇒ ab²acabc	[9]
16.	cb(ab)² ⇒ (a²c)²c	[20]
17.	cbc(ab)² ⇒ cac²	[22]
18.	cbacab² ⇒ abacabc²aba	[18]
19.	cbacabcb ⇒ ab(acabc)²	[23]
20.	ab²c(ab)² ⇒ abac²	[19]
21.	ab²acab² ⇒ c²aba	[16]
22.	ab²acabcb ⇒ (ca)²bc	[13]

# ab:aaabbbaba=ab ac/b abbb=c morph:4/0
aacaba=ab
aacabc=cb
cacaba=cb
abacaba=abb
cbb=abacabc
cbacaba=abacabc
ccabab=abbacc
aacabb=abcaba
cacabb=cbcaba
cacabcb=cbacabc
abbb=c
abbacaba=c
abcabab=aacc
abacabb=abbcaba
abacabcb=abbacabc
cbabab=aacaacc
cbcabab=cacc
cbacabb=abacabccaba
cbacabcb=abacabcacabc
abbcabab=abacc
abbacabb=ccaba
abbacabcb=cacabc