Termination proof

1: switching to dependency pairs

a____#( __( X , Y ) , Z )	→	a____#( mark( X ) , a____( mark( Y ) , mark( Z ) ) )
a____#( __( X , Y ) , Z )	→	mark#( X )
a____#( __( X , Y ) , Z )	→	a____#( mark( Y ) , mark( Z ) )
a____#( __( X , Y ) , Z )	→	mark#( Y )
a____#( __( X , Y ) , Z )	→	mark#( Z )
a____#( X , nil )	→	mark#( X )
a____#( nil , X )	→	mark#( X )
a__and#( tt , X )	→	mark#( X )
mark#( __( X1 , X2 ) )	→	a____#( mark( X1 ) , mark( X2 ) )
mark#( __( X1 , X2 ) )	→	mark#( X1 )
mark#( __( X1 , X2 ) )	→	mark#( X2 )
mark#( and( X1 , X2 ) )	→	a__and#( mark( X1 ) , X2 )
mark#( and( X1 , X2 ) )	→	mark#( X1 )
mark#( isNePal( X ) )	→	a__isNePal#( mark( X ) )
mark#( isNePal( X ) )	→	mark#( X )

1.1: dependency graph processor

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

• The 1st component contains the pair(s)

  a____#( __( X , Y ) , Z )	→	mark#( X )
  mark#( __( X1 , X2 ) )	→	a____#( mark( X1 ) , mark( X2 ) )
  a____#( __( X , Y ) , Z )	→	a____#( mark( X ) , a____( mark( Y ) , mark( Z ) ) )
  a____#( __( X , Y ) , Z )	→	a____#( mark( Y ) , mark( Z ) )
  a____#( __( X , Y ) , Z )	→	mark#( Y )
  mark#( __( X1 , X2 ) )	→	mark#( X1 )
  mark#( __( X1 , X2 ) )	→	mark#( X2 )
  mark#( and( X1 , X2 ) )	→	a__and#( mark( X1 ) , X2 )
  a__and#( tt , X )	→	mark#( X )
  mark#( and( X1 , X2 ) )	→	mark#( X1 )
  mark#( isNePal( X ) )	→	mark#( X )
  a____#( __( X , Y ) , Z )	→	mark#( Z )
  a____#( X , nil )	→	mark#( X )
  a____#( nil , X )	→	mark#( X )

  1.1.1: reduction pair processor

  Using the following reduction pair

  Linear polynomial interpretation over the naturals

  [__ (x1, x2) ]	=	2 x1 + x2 + 1
  [mark (x1) ]	=	x1
  [and (x1, x2) ]	=	2 x1 + 2 x2 + 2
  [isNePal (x1) ]	=	x1 + 3
  [a__isNePal (x1) ]	=	x1 + 3
  [a____ (x1, x2) ]	=	2 x1 + x2 + 1
  [a__and# (x1, x2) ]	=	2 x1 + x2
  [mark# (x1) ]	=	x1 + 2
  [a____# (x1, x2) ]	=	2 x1 + x2 + 2
  [nil]	=	2
  [tt]	=	2
  [a__and (x1, x2) ]	=	2 x1 + 2 x2 + 2
  [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.