Termination proof

1: switching to dependency pairs

The following set of initial dependency pairs has been identified.

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

1.1: reduction pair processor

Using the following reduction pair

Linear polynomial interpretation over the naturals
[g (x1, x2) ] = 2 x1 + 2 x2
[f (x1, x2) ] = 2 x1 + 2 x2 + 1
[f# (x1, x2) ] = 2 x1 + 3 x2
[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: P is empty

All dependency pairs have been removed.