Termination proof

1: switching to dependency pairs

The following set of initial dependency pairs has been identified.

dfib#( s( s( x ) ) , y ) → dfib#( s( x ) , dfib( x , y ) )
dfib#( s( s( x ) ) , y ) → dfib#( x , y )

1.1: reduction pair processor

Using the following reduction pair

Linear polynomial interpretation over the naturals
[s (x1) ] = 2 x1 + 3
[dfib (x1, x2) ] = 2 x1 + x2 + 3
[dfib# (x1, x2) ] = 3 x1 + 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.