⟨a, b | aabaaaab=aba⟩

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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 = aaaab
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.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	c¹⁸b ⇒ c²bc	[14]
2.	c⁴bc¹⁷b ⇒ c⁴(bc)²	[18]
3.	c⁸bc³bc¹⁷b ⇒ c⁸bc³(bc)²	[17]
4.	ac¹⁶b ⇒ abc	[5]
5.	ca ⇒ ac²	[4]
6.	c²ba ⇒ ac⁴bc	[10]
7.	c⁴bcba ⇒ ac⁸bc³bc	[16]
8.	c⁸bc³bcba ⇒ abc⁸bc³bc	[13]
9.	a²bc¹⁷b ⇒ a²(bc)²	[12]
10.	aba ⇒ a²bc	[3]
11.	a³bc³bc¹⁷b ⇒ a³bc³(bc)²	[15]
12.	a²bcba ⇒ a³bc³bc	[6]
13.	a⁴b ⇒ c	[2]
14.	a³bc³bcba ⇒ c⁸bc³bc	[11]

# ab:aabaaaab=aba bc/a aaaab=c morph:5/2 ccccccccccccccccccb=ccbc ccccbcccccccccccccccccb=ccccbcbc ccccccccbcccbcccccccccccccccccb=ccccccccbcccbcbc accccccccccccccccb=abc ca=acc ccba=accccbc ccccbcba=accccccccbcccbc ccccccccbcccbcba=abccccccccbcccbc aabcccccccccccccccccb=aabcbc aba=aabc aaabcccbcccccccccccccccccb=aaabcccbcbc aabcba=aaabcccbc aaaab=c aaabcccbcba=ccccccccbcccbc

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#4591 ⟨a, b | aabaaaab=aba⟩

Contents

Properties

Rewriting system