Term Rewriting System R:

   [x]
   f(s(x)) -> f(g(x, x))
   g(0, 1) -> s(0)
   0 -> 1

Innermost Termination of R to be shown.


Removing the following rules from R which left hand sides contain non normal subterms

   g(0, 1) -> s(0)

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

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

where the Polynomial interpretation:
POL(g(x_1, x_2)) = x_1 + x_2
POL(1) = 0
POL(s(x_1)) = 1 + 2*x_1
POL(f(x_1)) = 2 + x_1
POL(0) = 0
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: 

   0 -> 1

where the Polynomial interpretation:
POL(1) = 0
POL(0) = 1
was used. 



All Rules of R can be deleted.



Innermost Termination of R successfully shown.


Duration: 0.371 seconds.