Termination proof

1: switching to dependency pairs

evenodd#( x , 0 )	→	not#( evenodd( x , s( 0 ) ) )
evenodd#( x , 0 )	→	evenodd#( x , s( 0 ) )
evenodd#( s( x ) , s( 0 ) )	→	evenodd#( x , 0 )

1.1: dependency graph processor

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

• The 1st component contains the pair(s)

  evenodd#( s( x ) , s( 0 ) )	→	evenodd#( x , 0 )
  evenodd#( x , 0 )	→	evenodd#( x , s( 0 ) )

  1.1.1: reduction pair processor

  Using the following reduction pair

  Linear polynomial interpretation over the naturals

  [true]	=	0
  [false]	=	0
  [evenodd# (x1, x2) ]	=	x1
  [s (x1) ]	=	2 x1 + 2
  [0]	=	0
  [evenodd (x1, x2) ]	=	3
  [not (x1) ]	=	1
  [f(x1, ..., xn)]	=	x1 + ... + xn + 1	for all other symbols f of arity n

  one remains with the following pair(s).

  evenodd#( x , 0 )

  →

  evenodd#( x , s( 0 ) )

  1.1.1.1: dependency graph processor

  The dependency pairs are split into 0 component(s).