#4637 ⟨a, b | aababaab=aba⟩

Properties
Rewriting system

Properties

Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ ba = a²bc² and a ⋅ abc² = a²bc², however ba ≠ abc²

Rewriting system

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

#	Rule	Proof
1.	ca ⇒ ac⁴	[10]
2.	c¹²b ⇒ c⁴bc	[19]
3.	ac⁸b ⇒ abc	[18]
4.	c⁴ba ⇒ abc⁴	[13]
5.	aba ⇒ a²bc²	[16]
6.	a²bc¹⁰b ⇒ a²bc²bc	[11]
7.	a³bc²b ⇒ c	[17]
8.	a²bc²ba ⇒ c⁴	[12]

# ab:aababaab=aba c/ab aabab=c morph:5/1
ca=acccc
ccccccccccccb=ccccbc
accccccccb=abc
ccccba=abcccc
aba=aabcc
aabccccccccccb=aabccbc
aaabccb=c
aabccba=cccc

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#4637 ⟨a, b | aababaab=aba⟩

Contents

Properties

Rewriting system