Term Rewriting System R:

   [y, z, x]
   f(cons(nil, y)) -> y
   f(cons(f(cons(nil, y)), z)) -> copy(n, y, z)
   copy(0, y, z) -> f(z)
   copy(s(x), y, z) -> copy(x, y, cons(f(y), z))

Termination of R to be shown.


R contains the following Dependency Pairs: 


   COPY(s(x), y, z) -> COPY(x, y, cons(f(y), z))
   COPY(s(x), y, z) -> F(y)
   COPY(0, y, z) -> F(z)
   F(cons(f(cons(nil, y)), z)) -> COPY(n, y, z)

Furthermore, R contains one SCC.


SCC1:

COPY(s(x), y, z) -> COPY(x, y, cons(f(y), z))

By using a polynomial ordering, at least one Dependency Pair of this SCC can be strictly oriented.

No rules need to be oriented.

Used ordering: Polynomial ordering with Polynomial interpretation:
POL(nil) = 0
POL(s(x_1)) = 1 + x_1
POL(copy(x_1, x_2, x_3)) = 0
POL(f(x_1)) = 0
POL(COPY(x_1, x_2, x_3)) = x_1
POL(0) = 0
POL(cons(x_1, x_2)) = 0
POL(n) = 0

 resulting in no subcycles.




Termination of R successfully shown.


Duration: 0.566 seconds.