#4195 ⟨a, b | aabbbaaba=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.	aca²ba ⇒ ab	[3]
2.	aca²bc ⇒ cb	[4]
3.	c²a²ba ⇒ cb	[10]
4.	abca²ba ⇒ ab²	[5]
5.	cb² ⇒ abca²bc	[6]
6.	cbca²ba ⇒ abca²bc	[11]
7.	aca²b² ⇒ cba²ba	[8]
8.	c²a²bcb ⇒ cbca²bc	[13]
9.	ab³ ⇒ c	[2]
10.	ab²ca²ba ⇒ c	[7]
11.	abca²bcb ⇒ ab²ca²bc	[9]
12.	cba(ab)² ⇒ (ac)²	[14]
13.	cbca²bcb ⇒ ab(ca²bc)²	[15]
14.	ab²ca²bcb ⇒ c²a²bc	[12]

# ab:aabbbaaba=ab ac/b abbb=c morph:4/0
acaaba=ab
acaabc=cb
ccaaba=cb
abcaaba=abb
cbb=abcaabc
cbcaaba=abcaabc
acaabb=cbaaba
ccaabcb=cbcaabc
abbb=c
abbcaaba=c
abcaabcb=abbcaabc
cbaabab=acac
cbcaabcb=abcaabccaabc
abbcaabcb=ccaabc