Termination proof

1: switching to dependency pairs

The following set of initial dependency pairs has been identified.

fib#( s( s( x ) ) ) → fib#( s( x ) )
fib#( s( s( x ) ) ) → fib#( x )

1.1: reduction pair processor

Using the following reduction pair

Linear polynomial interpretation over the naturals
[fib# (x1) ] = x1
[+ (x1, x2) ] = 2 x1 + 3
[s (x1) ] = 3 x1 + 3
[fib (x1) ] = x1 + 2
[0] = 1
[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.