⟨a, b | aaababbaa=ab⟩

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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) = 0; deg(c) = 1; deg(b) = 2
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	a³bca² ⇒ ab	[3]
2.	cb ⇒ a³bcac	[4]
3.	ca²bca² ⇒ a³bcac	[7]
4.	ab² ⇒ c	[2]
5.	aba²bca² ⇒ c	[6]
6.	(a³b)²cac ⇒ c²a²	[9]
7.	a³bcab ⇒ (ab)²ca²	[5]
8.	caba³bcac ⇒ aba²bc³a²	[17]
9.	cabca²b ⇒ aba²bc²	[14]
10.	ca²ba³bcac ⇒ aba²bcac²a²	[12]
11.	ca²bcab ⇒ a³b(ca)²bca²	[11]
12.	(ab)²a³bcac ⇒ a³bc³a²	[15]
13.	(ab)²ca²b ⇒ a³bc²	[13]
14.	aba²ba³bcac ⇒ a³bcac²a²	[10]
15.	aba²bcab ⇒ cabca²	[8]
16.	a³baba²bc² ⇒ (ab)²(ca²)²b	[16]
17.	a³baba²bcac ⇒ c²a²b	[19]
18.	c(ab)²a²bcac ⇒ aba²bc³a²b	[22]
19.	ca(ab)²a²bc² ⇒ a³b(ca)²b(ca²)²b	[24]
20.	ca(ab)²a²bcac ⇒ aba²bcac²a²b	[23]
21.	(ab)³a²bcac ⇒ a³bc³a²b	[20]
22.	(aba²b)²c² ⇒ cab(ca²)²b	[18]
23.	(aba²b)²cac ⇒ a³bcac²a²b	[21]

# ab:aaababbaa=ab a/c/b abb=c morph:3/0 aaabcaa=ab cb=aaabcac caabcaa=aaabcac abb=c abaabcaa=c aaabaaabcac=ccaa aaabcab=ababcaa cabaaabcac=abaabcccaa cabcaab=abaabcc caabaaabcac=abaabcaccaa caabcab=aaabcacabcaa ababaaabcac=aaabcccaa ababcaab=aaabcc abaabaaabcac=aaabcaccaa abaabcab=cabcaa aaababaabcc=ababcaacaab aaababaabcac=ccaab cababaabcac=abaabcccaab caababaabcc=aaabcacabcaacaab caababaabcac=abaabcaccaab abababaabcac=aaabcccaab abaababaabcc=cabcaacaab abaababaabcac=aaabcaccaab

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#3999 ⟨a, b | aaababbaa=ab⟩

Contents

Properties

Rewriting system