⟨a, b | aabbaa=abab⟩

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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 = abab
Reduction order:
- Left-to-right recursive path with deg(a) = 0; deg(b) = deg(c) = 1, b < c
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	(ab)² ⇒ c	[2]
2.	a²b²a² ⇒ c	[3]
3.	cab ⇒ abc	[4]
4.	abcba² ⇒ a²b²ac	[6]
5.	cb²a² ⇒ a²b²c	[5]
6.	cbab ⇒ a²b²ac	[7]
7.	aba²b²ac ⇒ c²ba²	[9]
8.	ca²b²ac ⇒ abc²ba²	[10]
9.	(cb)²a² ⇒ abcbac	[8]
10.	c²ba³b ⇒ a(bc)²	[12]
11.	cba²b²ac ⇒ a²b²ac²ba²	[11]
12.	a²(b²ac)² ⇒ c(cba²)²	[15]
13.	c²ba⁴b²ac ⇒ abcbc²ba²	[14]
14.	c(cba²)²ab ⇒ a(bc)³	[13]
15.	abcbacb²ac ⇒ a²b²ac(cba²)²	[16]
16.	c(b²ac)² ⇒ a²b²c(cba²)²	[18]
17.	c(cba²)³ ⇒ c²bacb²ac	[20]
18.	(cb)²acb²ac ⇒ abcbac(cba²)²	[19]
19.	c(cba²)²a²b²ac ⇒ a(bc)³cba²	[17]
20.	c²ba(acb)²bac ⇒ c²bacb²ac²ba²	[21]
21.	c²b(a²cb)²acb²ac ⇒ c²bacb²ac(cba²)²	[22]

# ab:aabbaa=abab a/bc abab=c magic:0 abab=c aabbaa=c cab=abc abcbaa=aabbac cbbaa=aabbc cbab=aabbac abaabbac=ccbaa caabbac=abccbaa cbcbaa=abcbac ccbaaab=abcbc cbaabbac=aabbaccbaa aabbacbbac=ccbaacbaa ccbaaaabbac=abcbccbaa ccbaacbaaab=abcbcbc abcbacbbac=aabbaccbaacbaa cbbacbbac=aabbccbaacbaa ccbaacbaacbaa=ccbacbbac cbcbacbbac=abcbaccbaacbaa ccbaacbaaaabbac=abcbcbccbaa ccbaacbacbbac=ccbacbbaccbaa ccbaacbaacbacbbac=ccbacbbaccbaacbaa

Up:	Monoids with two generators and one relation
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Next:	#2526 ⟨a, b \| aabbaa=abba⟩

#2525 ⟨a, b | aabbaa=abab⟩

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