Term Rewriting System R:

   [X, Y]
   f(c(X, s(Y))) -> f(c(s(X), Y))
   g(c(s(X), Y)) -> f(c(X, s(Y)))

Termination of R to be shown.


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

   f(c(X, s(Y))) -> f(c(s(X), Y))

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

   g(c(s(X), Y)) -> f(c(X, s(Y)))

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



All Rules of R can be deleted.



Termination of R successfully shown.


Duration: 0.400 seconds.