Term Rewriting System R:

   [x]
   app(f, app(f, x)) -> app(g, app(f, x))
   app(g, app(g, x)) -> app(f, x)

Termination of R to be shown.


Removing the following rules from R which fullfill a polynomial ordering: 

   app(f, app(f, x)) -> app(g, app(f, x))

where the Polynomial interpretation:
POL(g) = 1
POL(f) = 2
POL(app(x_1, x_2)) = x_1 + x_2
was used. 



Not all Rules of R can be deleted, so we still have to regard a part of R.


Removing the following rules from R which fullfill a polynomial ordering: 

   app(g, app(g, x)) -> app(f, x)

where the Polynomial interpretation:
POL(g) = 1
POL(f) = 0
POL(app(x_1, x_2)) = x_1 + x_2
was used. 



All Rules of R can be deleted.



Termination of R successfully shown.


Duration: 0.369 seconds.