Termination proof

1: switching to dependency pairs

a__g#( X )	→	a__h#( X )
a__h#( d )	→	a__g#( c )
mark#( g( X ) )	→	a__g#( X )
mark#( h( X ) )	→	a__h#( X )
mark#( c )	→	a__c#

1.1: dependency graph processor

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

• The 1st component contains the pair(s)

  a__h#( d )	→	a__g#( c )
  a__g#( X )	→	a__h#( X )

  1.1.1: reduction pair processor

  Using the following reduction pair

  Linear polynomial interpretation over the naturals

  [d]	=	1
  [h (x1) ]	=	2 x1 + 1
  [a__g (x1) ]	=	3 x1 + 3
  [mark (x1) ]	=	2 x1 + 2
  [c]	=	0
  [a__g# (x1) ]	=	x1 + 1
  [a__h (x1) ]	=	2 x1 + 3
  [a__c]	=	1
  [a__h# (x1) ]	=	x1 + 1
  [g (x1) ]	=	2 x1 + 2
  [f(x1, ..., xn)]	=	x1 + ... + xn + 1	for all other symbols f of arity n

  one remains with the following pair(s).

  a__g#( X )

  →

  a__h#( X )

  1.1.1.1: dependency graph processor

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