⟨a, b | abaaab=aabba⟩

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Monoids with two generators and one relation

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

Auxiliary generators:
1. c = aba
Reduction order:
- Left-to-right recursive path with deg(a) = deg(c) = 0, a < c; deg(b) = 1
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	aba ⇒ c	[2]
2.	cba ⇒ abc	[4]
3.	a²b²a ⇒ ca²b	[3]
4.	a²b²c ⇒ c²a²b	[6]
5.	cab²a ⇒ abca²b	[7]
6.	cab²c ⇒ abc²a²b	[9]
7.	cacb²a ⇒ c(ca)²b	[10]
8.	cacb²ca ⇒ c²a²bcac	[13]
9.	c(ca²b)² ⇒ cacb²c	[8]
10.	c²ac²b²a ⇒ c²a²b(ca)²b	[12]
11.	c²ac²b²ca ⇒ cacb²c²ac	[15]
12.	cacb(bc)² ⇒ c²a²bc³a²b	[14]
13.	cacb²c²a²b ⇒ c²ac²b²c	[11]
14.	c²a²bcac²b²a ⇒ cacb²c(ca)²b	[16]
15.	c²a²bcac²b²ca ⇒ c²ac²b²c²ac	[17]
16.	c²ac²b(bc)² ⇒ cacb²c⁴a²b	[19]
17.	c²ac²b²c²a²b ⇒ c²a²bcac²b²c	[18]
18.	c²a²bcac²b(bc)² ⇒ c²ac²b²c⁴a²b	[21]
19.	c²a²bcac²b²c²a²b ⇒ cacb²c²ac²b²c	[20]

# ab:abaaab=aabba ac/b aba=c morph:3/0 aba=c cba=abc aabba=caab aabbc=ccaab cabba=abcaab cabbc=abccaab cacbba=ccacab cacbbca=ccaabcac ccaabcaab=cacbbc ccaccbba=ccaabcacab ccaccbbca=cacbbccac cacbbcbc=ccaabcccaab cacbbccaab=ccaccbbc ccaabcaccbba=cacbbccacab ccaabcaccbbca=ccaccbbccac ccaccbbcbc=cacbbccccaab ccaccbbccaab=ccaabcaccbbc ccaabcaccbbcbc=ccaccbbccccaab ccaabcaccbbccaab=cacbbccaccbbc

Up:	Monoids with two generators and one relation
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#5815 ⟨a, b | abaaab=aabba⟩

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