Termination proof

1: switching to dependency pairs

mem#( x , union( y , z ) )	→	or#( mem( x , y ) , mem( x , z ) )
mem#( x , union( y , z ) )	→	mem#( x , y )
mem#( x , union( y , z ) )	→	mem#( x , z )

1.1: dependency graph processor

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

• The 1st component contains the pair(s)

  mem#( x , union( y , z ) )	→	mem#( x , z )
  mem#( x , union( y , z ) )	→	mem#( x , y )

  1.1.1: reduction pair processor

  Using the following reduction pair

  Linear polynomial interpretation over the naturals

  [true]	=	0
  [union (x1, x2) ]	=	2 x1 + 2 x2 + 3
  [false]	=	1
  [or (x1, x2) ]	=	x1 + x2 + 1
  [= (x1, x2) ]	=	x1 + 1
  [mem# (x1, x2) ]	=	x1
  [mem (x1, x2) ]	=	3 x1 + 1
  [nil]	=	0
  [set (x1) ]	=	2 x1 + 3
  [f(x1, ..., xn)]	=	x1 + ... + xn + 1	for all other symbols f of arity n

  one remains with the following pair(s).

  none

  1.1.1.1: P is empty

  All dependency pairs have been removed.