Term Rewriting System R:
[x, y, z, u, v]
f(x, y, f(z, u, v)) -> f(f(x, y, z), u, f(x, y, v))

Termination of R to be shown. 



   R
     ↳Dependency Pair Analysis



R contains the following Dependency Pairs:

F(x, y, f(z, u, v)) -> F(f(x, y, z), u, f(x, y, v))
F(x, y, f(z, u, v)) -> F(x, y, z)
F(x, y, f(z, u, v)) -> F(x, y, v)

Furthermore, R contains one SCC. 


   R
     ↳DPs
       →DP Problem 1
         ↳Non Termination


Dependency Pairs:

F(x, y, f(z, u, v)) -> F(x, y, v)
F(x, y, f(z, u, v)) -> F(x, y, z)
F(x, y, f(z, u, v)) -> F(f(x, y, z), u, f(x, y, v))


Rule:


f(x, y, f(z, u, v)) -> f(f(x, y, z), u, f(x, y, v))





Found an infinite P-chain over R:
P =

F(x, y, f(z, u, v)) -> F(x, y, v)
F(x, y, f(z, u, v)) -> F(x, y, z)
F(x, y, f(z, u, v)) -> F(f(x, y, z), u, f(x, y, v))

R =

f(x, y, f(z, u, v)) -> f(f(x, y, z), u, f(x, y, v))

s = F(x, y, f(z, u, v))
evaluates to t =F(f(x, y, z), u, f(x, y, v))

Thus, s starts an infinite chain as s matches t.

Non-Termination of R could be shown.
Duration:
0:00 minutes