#4015 ⟨a, b | aaabbaaba=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. abb=c
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	c²a²ba ⇒ ab(ac)²	[10]
2.	a²ca²ba ⇒ ab	[3]
3.	a²ca²bc ⇒ cb	[4]
4.	caca²ba ⇒ cb	[8]
5.	ab² ⇒ c	[2]
6.	abca²ba ⇒ a(ac)²	[7]
7.	abaca²ba ⇒ c	[5]
8.	cb² ⇒ abaca²bc	[6]
9.	cba²ba ⇒ (a²ca)²c	[15]
10.	cbca²ba ⇒ c(ac)²	[13]
11.	cbaca²ba ⇒ abaca²bc	[11]
12.	c²a²bcb ⇒ ab(ac)³a²bc	[14]
13.	caca²bcb ⇒ cbaca²bc	[12]
14.	abca²bcb ⇒ a(ac)³a²bc	[16]
15.	abaca²bcb ⇒ caca²bc	[9]
16.	cba²bcb ⇒ a²ca³(ca)³abc	[18]
17.	cbca²bcb ⇒ (ca)⁴abc	[17]
18.	cbaca²bcb ⇒ ab(aca²bc)²	[19]

# ab:aaabbaaba=ab ac/b abb=c morph:3/0
ccaaba=abacac
aacaaba=ab
aacaabc=cb
cacaaba=cb
abb=c
abcaaba=aacac
abacaaba=c
cbb=abacaabc
cbaaba=aacaaacac
cbcaaba=cacac
cbacaaba=abacaabc
ccaabcb=abacacacaabc
cacaabcb=cbacaabc
abcaabcb=aacacacaabc
abacaabcb=cacaabc
cbaabcb=aacaaacacacaabc
cbcaabcb=cacacacaabc
cbacaabcb=abacaabcacaabc