Termination proof

1: switching to dependency pairs

a__f#( X , X )	→	a__f#( a , b )
mark#( f( X1 , X2 ) )	→	a__f#( mark( X1 ) , X2 )
mark#( f( X1 , X2 ) )	→	mark#( X1 )
mark#( b )	→	a__b#

1.1: dependency graph processor

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

• The 1st component contains the pair(s)

  mark#( f( X1 , X2 ) )

  →

  mark#( X1 )

  1.1.1: reduction pair processor

  Using the following reduction pair

  Linear polynomial interpretation over the naturals

  [b]	=	0
  [a]	=	0
  [mark (x1) ]	=	2 x1
  [f (x1, x2) ]	=	2 x1 + 2 x2 + 2
  [mark# (x1) ]	=	x1
  [a__f (x1, x2) ]	=	2 x1 + 3 x2 + 2
  [a__b]	=	0
  [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.