Termination proof

1: switching to dependency pairs

f#( f( x ) )	→	f#( g( f( x ) , x ) )
f#( f( x ) )	→	g#( f( x ) , x )
f#( f( x ) )	→	f#( x )
f#( f( x ) )	→	f#( h( f( x ) , f( x ) ) )
f#( f( x ) )	→	h#( f( x ) , f( x ) )
f#( f( x ) )	→	f#( x )
f#( f( x ) )	→	f#( x )
h#( x , x )	→	g#( x , 0 )

1.1: dependency graph processor

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

• The 1st component contains the pair(s)

  f#( f( x ) )	→	f#( x )
  f#( f( x ) )	→	f#( g( f( x ) , x ) )
  f#( f( x ) )	→	f#( h( f( x ) , f( x ) ) )

  1.1.1: reduction pair processor

  Using the following reduction pair

  Linear polynomial interpretation over the naturals

  [g (x1, x2) ]	=	x1 + 1
  [f (x1) ]	=	3 x1 + 2
  [0]	=	0
  [f# (x1) ]	=	x1
  [h (x1, x2) ]	=	1
  [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.