Termination proof

1: switching to dependency pairs

The following set of initial dependency pairs has been identified.

implies#( not( x ) , or( y , z ) ) → implies#( y , or( x , z ) )
implies#( x , or( y , z ) ) → implies#( x , z )

1.1: reduction pair processor

Using the following reduction pair

Linear polynomial interpretation over the naturals
[implies# (x1, x2) ] = 3 x1
[or (x1, x2) ] = 3 x1 + 3
[implies (x1, x2) ] = 3 x1 + 3
[not (x1) ] = 0
[f(x1, ..., xn)] = x1 + ... + xn + 1 for all other symbols f of arity n

one remains with the following pair(s).

implies#( not( x ) , or( y , z ) ) → implies#( y , or( x , z ) )

1.1.1: reduction pair processor

Using the following reduction pair

Linear polynomial interpretation over the naturals
[implies# (x1, x2) ] = 3 x1 + 3 x2
[or (x1, x2) ] = 3 x1 + 1
[implies (x1, x2) ] = x1 + x2 + 3
[not (x1) ] = 3 x1 + 1
[f(x1, ..., xn)] = x1 + ... + xn + 1 for all other symbols f of arity n

one remains with the following pair(s).

none

1.1.1.1: P is empty

All dependency pairs have been removed.