Termination proof

1: switching to dependency pairs

concat#( cons( U , V ) , Y )	→	concat#( V , Y )
lessleaves#( cons( U , V ) , cons( W , Z ) )	→	lessleaves#( concat( U , V ) , concat( W , Z ) )
lessleaves#( cons( U , V ) , cons( W , Z ) )	→	concat#( U , V )
lessleaves#( cons( U , V ) , cons( W , Z ) )	→	concat#( W , Z )

1.1: dependency graph processor

The dependency pairs are split into 2 component(s).

• The 1st component contains the pair(s)

  lessleaves#( cons( U , V ) , cons( W , Z ) )

  →

  lessleaves#( concat( U , V ) , concat( W , Z ) )

  1.1.1: reduction pair processor

  Using the following reduction pair

  Linear polynomial interpretation over the naturals

  [concat (x1, x2) ]	=	x1 + x2 + 1
  [true]	=	0
  [leaf]	=	0
  [false]	=	0
  [lessleaves (x1, x2) ]	=	1
  [lessleaves# (x1, x2) ]	=	2 x1
  [cons (x1, x2) ]	=	2 x1 + 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.

• The 2nd component contains the pair(s)

  concat#( cons( U , V ) , Y )

  →

  concat#( V , Y )

  1.1.2: reduction pair processor

  Using the following reduction pair

  Linear polynomial interpretation over the naturals

  [concat (x1, x2) ]	=	2 x1 + x2 + 2
  [true]	=	0
  [leaf]	=	0
  [false]	=	0
  [lessleaves (x1, x2) ]	=	1
  [concat# (x1, x2) ]	=	x1
  [cons (x1, x2) ]	=	2 x1 + x2 + 3
  [f(x1, ..., xn)]	=	x1 + ... + xn + 1	for all other symbols f of arity n

  one remains with the following pair(s).

  none

  1.1.2.1: P is empty

  All dependency pairs have been removed.