Termination proof

1: switching to dependency pairs

concat#( cons( u , v ) , y )	→	concat#( v , y )
less_leaves#( cons( u , v ) , cons( w , z ) )	→	less_leaves#( concat( u , v ) , concat( w , z ) )
less_leaves#( cons( u , v ) , cons( w , z ) )	→	concat#( u , v )
less_leaves#( 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)

  less_leaves#( cons( u , v ) , cons( w , z ) )

  →

  less_leaves#( 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
  [true]	=	2
  [less_leaves# (x1, x2) ]	=	2 x1
  [leaf]	=	0
  [false]	=	0
  [less_leaves (x1, x2) ]	=	2 x1
  [cons (x1, x2) ]	=	2 x1 + x2 + 2
  [x]	=	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.

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

  one remains with the following pair(s).

  none

  1.1.2.1: P is empty

  All dependency pairs have been removed.