Term Rewriting System R:

   [y, x, f]
   app(app(plus, 0), y) -> y
   app(app(plus, app(s, x)), y) -> app(s, app(app(plus, x), y))
   app(app(app(curry, f), x), y) -> app(app(f, x), y)
   add -> app(curry, plus)

Termination of R to be shown.


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

   app(app(plus, 0), y) -> y

where the Polynomial interpretation:
POL(add) = 0
POL(plus) = 0
POL(s) = 0
POL(curry) = 0
POL(app(x_1, x_2)) = x_1 + x_2
POL(0) = 1
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(app(plus, app(s, x)), y) -> app(s, app(app(plus, x), y))

where the Polynomial interpretation:
POL(add) = 0
POL(plus) = 0
POL(s) = 1
POL(curry) = 0
POL(app(x_1, x_2)) = 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(app(app(curry, f), x), y) -> app(app(f, x), y)

where the Polynomial interpretation:
POL(add) = 1
POL(plus) = 0
POL(curry) = 0
POL(app(x_1, x_2)) = 1 + 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: 

   add -> app(curry, plus)

where the Polynomial interpretation:
POL(add) = 1
POL(plus) = 0
POL(curry) = 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: 0.420 seconds.