Termination proof

1: switching to dependency pairs

merge#( ++( x , y ) , ++( u , v ) )	→	merge#( y , ++( u , v ) )
merge#( ++( x , y ) , ++( u , v ) )	→	merge#( ++( x , y ) , v )

1.1: dependency graph processor

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

• The 1st component contains the pair(s)

  merge#( ++( x , y ) , ++( u , v ) )

  →

  merge#( y , ++( u , v ) )

  1.1.1: reduction pair processor

  Using the following reduction pair

  Linear polynomial interpretation over the naturals

  [v]	=	2
  [++ (x1, x2) ]	=	x1 + 2
  [u]	=	0
  [merge# (x1, x2) ]	=	x1
  [merge (x1, x2) ]	=	2 x1 + 2 x2
  [nil]	=	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.