Termination proof

1: switching to dependency pairs

f#( f( x ) )	→	f#( c( f( x ) ) )
f#( f( x ) )	→	f#( x )
f#( f( x ) )	→	f#( d( f( x ) ) )
f#( f( x ) )	→	f#( x )
g#( c( 0 ) )	→	g#( d( 1 ) )
g#( c( 1 ) )	→	g#( d( 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 )

  1.1.1: reduction pair processor

  Using the following reduction pair

  Linear polynomial interpretation over the naturals

  [f (x1) ]	=	2 x1 + 1
  [d (x1) ]	=	x1
  [c (x1) ]	=	x1
  [1]	=	0
  [0]	=	0
  [f# (x1) ]	=	3 x1
  [g (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.