Termination proof

1: switching to dependency pairs

f#( n__f( n__a ) )	→	f#( n__g( n__f( n__a ) ) )
activate#( n__f( X ) )	→	f#( X )
activate#( n__a )	→	a#
activate#( n__g( X ) )	→	g#( activate( X ) )
activate#( n__g( X ) )	→	activate#( X )

1.1: dependency graph processor

The dependency pairs are split into 1 component(s).

• The 1st component contains the pair(s)

  activate#( n__g( X ) )

  →

  activate#( X )

  1.1.1: reduction pair processor

  Using the following reduction pair

  Linear polynomial interpretation over the naturals

  [n__a]	=	1
  [a]	=	1
  [activate# (x1) ]	=	3 x1
  [f (x1) ]	=	3
  [n__g (x1) ]	=	2 x1 + 2
  [n__f (x1) ]	=	2
  [g (x1) ]	=	2 x1 + 2
  [activate (x1) ]	=	2 x1
  [f(x1, ..., xn)]	=	x1 + ... + xn + 1	for all other symbols f of arity n

  one remains with the following pair(s).

  none

  1.1.1.1: P is empty

  All dependency pairs have been removed.