Termination proof

1: switching to dependency pairs

The following set of initial dependency pairs has been identified.

h#( f( x ) , y ) → g#( x , y )
g#( x , y ) → h#( x , y )

1.1: reduction pair processor

Using the following reduction pair

Linear polynomial interpretation over the naturals
[g# (x1, x2) ] = 2 x1
[g (x1, x2) ] = 3 x1 + 2
[h# (x1, x2) ] = 2 x1
[f (x1) ] = x1 + 3
[h (x1, x2) ] = 3 x1
[f(x1, ..., xn)] = x1 + ... + xn + 1 for all other symbols f of arity n

one remains with the following pair(s).

g#( x , y ) → h#( x , y )

1.1.1: dependency graph processor

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