Term Rewriting System R:

   [Z, X, Y]
   fst(0, Z) -> nil
   fst(s(X), cons(Y, Z)) -> cons(Y, fst(X, Z))
   from(X) -> cons(X, from(s(X)))
   add(0, X) -> X
   add(s(X), Y) -> s(add(X, Y))
   len(nil) -> 0
   len(cons(X, Z)) -> s(len(Z))

Termination of R to be shown.


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


R contains the following Dependency Pairs: 


   FROM(X) -> FROM(s(X))
   ADD(s(X), Y) -> ADD(X, Y)
   LEN(cons(X, Z)) -> LEN(Z)
   FST(s(X), cons(Y, Z)) -> FST(X, Z)

Furthermore, R contains four SCCs.


SCC1:

FROM(X) -> FROM(s(X))

Found an infinite P-chain over R:
P = FROM(X) -> FROM(s(X))
R = []
s = FROM(X) evaluates to t = FROM(s(X))
Thus, s starts an infinite reduction as s matches t.


Non-Termination of R could be shown.

Duration: 0.546 seconds.