Term Rewriting System R:

   [x, y]
   f(s(x)) -> f(x)
   g(cons(0, y)) -> g(y)
   g(cons(s(x), y)) -> s(x)
   h(cons(x, y)) -> h(g(cons(x, y)))

Termination of R to be shown.


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

   f(s(x)) -> f(x)
   g(cons(0, y)) -> g(y)

where the Polynomial interpretation:
POL(g(x_1)) = x_1
POL(s(x_1)) = 1 + x_1
POL(h(x_1)) = 1 + x_1
POL(f(x_1)) = 2 + x_1
POL(0) = 1
POL(cons(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: 

   g(cons(s(x), y)) -> s(x)

where the Polynomial interpretation:
POL(g(x_1)) = x_1
POL(s(x_1)) = 1 + x_1
POL(h(x_1)) = 1 + x_1
POL(cons(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.


This program has no overlaps, so it is sufficient to show innermost termination. 


R contains the following Dependency Pairs: 


   H(cons(x, y)) -> H(g(cons(x, y)))

R contains no SCCs.




Termination of R successfully shown.


Duration: 0.442 seconds.