Termination proof

1: switching to dependency pairs

The following set of initial dependency pairs has been identified.

app#( app( app( compose , f ) , g ) , x ) → app#( f , app( g , x ) )
app#( app( app( compose , f ) , g ) , x ) → app#( g , x )

1.1: reduction pair processor

Using the following reduction pair

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