Termination proof

1: switching to dependency pairs

U11#( tt , M , N )	→	U12#( tt , activate( M ) , activate( N ) )
U11#( tt , M , N )	→	activate#( M )
U11#( tt , M , N )	→	activate#( N )
U12#( tt , M , N )	→	plus#( activate( N ) , activate( M ) )
U12#( tt , M , N )	→	activate#( N )
U12#( tt , M , N )	→	activate#( M )
plus#( N , s( M ) )	→	U11#( tt , M , N )

1.1: dependency graph processor

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

• The 1st component contains the pair(s)

  U12#( tt , M , N )	→	plus#( activate( N ) , activate( M ) )
  plus#( N , s( M ) )	→	U11#( tt , M , N )
  U11#( tt , M , N )	→	U12#( tt , activate( M ) , activate( N ) )

  1.1.1: reduction pair processor

  Using the following reduction pair

  Linear polynomial interpretation over the naturals

  [U11 (x1, x2, x3) ]	=	2 x1 + x2 + x3
  [U11# (x1, x2, x3) ]	=	3 x1 + 2 x2 + 2
  [plus (x1, x2) ]	=	x1 + x2 + 1
  [s (x1) ]	=	x1 + 3
  [U12 (x1, x2, x3) ]	=	2 x1 + x2 + x3
  [0]	=	0
  [plus# (x1, x2) ]	=	2 x1 + 3
  [U12# (x1, x2, x3) ]	=	2 x1 + 3
  [tt]	=	2
  [activate (x1) ]	=	x1
  [f(x1, ..., xn)]	=	x1 + ... + xn + 1	for all other symbols f of arity n

  one remains with the following pair(s).

  U12#( tt , M , N )

  →

  plus#( activate( N ) , activate( M ) )

  1.1.1.1: dependency graph processor

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