Termination proof

1: switching to dependency pairs

f#( f( X ) )	→	f#( a( b( f( X ) ) ) )
f#( f( X ) )	→	b#( f( X ) )
f#( f( X ) )	→	f#( X )
f#( a( g( X ) ) )	→	b#( X )

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 )

  1.1.1: reduction pair processor

  Using the following reduction pair

  Linear polynomial interpretation over the naturals

  [a (x1) ]	=	x1
  [b (x1) ]	=	x1
  [f (x1) ]	=	2 x1 + 1
  [f# (x1) ]	=	x1
  [g (x1) ]	=	x1 + 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.