⟨a, b | abbaab=ababa⟩

Up:

Format:	Pretty Plain
Word:
	Enter a word above to compute its normal form. Tips: Lowercase letters stand for generators. Spaces are ignored. Numbers repeat the previous letter, e.g. `b90`.
Strategy:	Leftmost Rightmost
Result:	1 1

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

#	Rule	Proof
1.	c³b ⇒ cbc²	[17]
2.	cba ⇒ abc	[4]
3.	c²ab ⇒ abc²	[8]
4.	cbcab ⇒ cb²ac	[9]
5.	c³ac²b ⇒ cabc⁴	[28]
6.	cbc²a ⇒ abc³	[16]
7.	c⁵a ⇒ c³ac²	[26]
8.	cbc⁴a ⇒ abc⁵	[19]
9.	abcab ⇒ ab²ac	[5]
10.	abc²ac²b ⇒ (ab)²c⁴	[18]
11.	abc⁴a ⇒ abc²ac²	[22]
12.	caba ⇒ ab²ac	[6]
13.	cab²ac ⇒ abc²a	[11]
14.	cabc²a ⇒ ab²ac³	[14]
15.	cb²a²b ⇒ (ab)²c	[7]
16.	cb²aca ⇒ abcb²ac	[12]
17.	c(b²ac)² ⇒ abc³a	[32]
18.	cb²ac³a ⇒ abcb²ac³	[23]
19.	c³a² ⇒ abc²b²ac	[29]
20.	c³acab ⇒ ab²ac⁴	[20]
21.	c(c²a)² ⇒ abc²b²ac³	[31]
22.	c³ac⁴a ⇒ abc²b²ac⁵	[33]
23.	a(ba)² ⇒ c	[2]
24.	(ab)²c²a ⇒ c³	[13]
25.	ab²a²b ⇒ c	[3]
26.	ab²aca ⇒ abab²ac	[10]
27.	ab²ac³a ⇒ abab²ac³	[21]
28.	abc²a² ⇒ a(b²ac)²	[25]
29.	abc(ca)²b ⇒ c⁴	[15]
30.	ab(c²a)² ⇒ a(b²ac)²c²	[30]
31.	abc²ac⁴a ⇒ a(b²ac)²c⁴	[34]
32.	aba(b²ac)² ⇒ c³a	[24]

# ab:abbaab=ababa bc/a ababa=c magic:0 cccb=cbcc cba=abc ccab=abcc cbcab=cbbac cccaccb=cabcccc cbcca=abccc ccccca=cccacc cbcccca=abccccc abcab=abbac abccaccb=ababcccc abcccca=abccacc caba=abbac cabbac=abcca cabcca=abbaccc cbbaab=ababc cbbaca=abcbbac cbbacbbac=abccca cbbaccca=abcbbaccc cccaa=abccbbac cccacab=abbacccc cccacca=abccbbaccc cccacccca=abccbbaccccc ababa=c ababcca=ccc abbaab=c abbaca=ababbac abbaccca=ababbaccc abccaa=abbacbbac abccacab=cccc abccacca=abbacbbaccc abccacccca=abbacbbaccccc ababbacbbac=ccca

Up:	Monoid enumeration
Prev:	#5917 ⟨a, b \| abbaab=abaab⟩
Next:	#5919 ⟨a, b \| abbaab=abbaa⟩

#5918 ⟨a, b | abbaab=ababa⟩

Contents

Properties

Rewriting system