Term Rewriting System R:

   [x, y, z]
   f(x, y, z) -> g(<=(x, y), x, y, z)
   g(true, x, y, z) -> z
   g(false, x, y, z) -> f(f(p(x), y, z), f(p(y), z, x), f(p(z), x, y))
   p(0) -> 0
   p(s(x)) -> x

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: 


   F(x, y, z) -> G(<=(x, y), x, y, z)
   G(false, x, y, z) -> F(f(p(x), y, z), f(p(y), z, x), f(p(z), x, y))
   G(false, x, y, z) -> F(p(x), y, z)
   G(false, x, y, z) -> P(x)
   G(false, x, y, z) -> F(p(y), z, x)
   G(false, x, y, z) -> P(y)
   G(false, x, y, z) -> F(p(z), x, y)
   G(false, x, y, z) -> P(z)

R contains no SCCs.




Termination of R successfully shown.


Duration: 0.502 seconds.