⟨a, b | aaabbabaa=ab⟩

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 = abb
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.	a²caba² ⇒ ab	[3]
2.	a²cabac ⇒ cb	[4]
3.	(ca)²ba² ⇒ cb	[9]
4.	ab² ⇒ c	[2]
5.	abacaba² ⇒ c	[6]
6.	cb² ⇒ (abac)²	[8]
7.	cbaba² ⇒ a²c²	[10]
8.	cbacaba² ⇒ (abac)²	[14]
9.	c²aba²b ⇒ abacabc	[25]
10.	a²c(ab)² ⇒ abcaba²	[5]
11.	a²cabcb ⇒ abcabac	[7]
12.	cac(ab)² ⇒ cbcaba²	[15]
13.	(ca)²bcb ⇒ cbcabac	[16]
14.	(ca)²bacb ⇒ cbacabac	[17]
15.	abcaba²b ⇒ a²cabc	[21]
16.	abac(ab)² ⇒ c²aba²	[11]
17.	abacabcb ⇒ c²abac	[12]
18.	(abac)²b ⇒ (ca)²bac	[13]
19.	cb(ab)² ⇒ a²c³aba²	[18]
20.	cbabcb ⇒ a²c³abac	[19]
21.	c(ba)²cb ⇒ a²c(ca)²bac	[20]
22.	cbcaba²b ⇒ (ca)²bc	[24]
23.	cbac(ab)² ⇒ (abac)²caba²	[22]
24.	cbacabcb ⇒ aba(cabac)²	[23]
25.	cbacabacb ⇒ ab(acabac)²	[26]

# ab:aaabbabaa=ab ac/b abb=c morph:3/0 aacabaa=ab aacabac=cb cacabaa=cb abb=c abacabaa=c cbb=abacabac cbabaa=aacc cbacabaa=abacabac ccabaab=abacabc aacabab=abcabaa aacabcb=abcabac cacabab=cbcabaa cacabcb=cbcabac cacabacb=cbacabac abcabaab=aacabc abacabab=ccabaa abacabcb=ccabac abacabacb=cacabac cbabab=aacccabaa cbabcb=aacccabac cbabacb=aaccacabac cbcabaab=cacabc cbacabab=abacabaccabaa cbacabcb=abacabaccabac cbacabacb=abacabacacabac

Up:	Monoid enumeration
Prev:	#4022 ⟨a, b \| aaabbabaa=aa⟩
Next:	#4024 ⟨a, b \| aaabbabaa=ba⟩

#4023 ⟨a, b | aaabbabaa=ab⟩

Contents

Properties

Rewriting system