Term Rewriting System R:
[x, y, z]
f(s(a), s(b), x) -> f(x, x, x)
g(f(s(x), s(y), z)) -> g(f(x, y, z))
cons(x, y) -> x
cons(x, y) -> y

Termination of R to be shown.

`   R`
`     ↳Dependency Pair Analysis`

R contains the following Dependency Pairs:

F(s(a), s(b), x) -> F(x, x, x)
G(f(s(x), s(y), z)) -> G(f(x, y, z))
G(f(s(x), s(y), z)) -> F(x, y, z)

Furthermore, R contains two SCCs.

`   R`
`     ↳DPs`
`       →DP Problem 1`
`         ↳Non Termination`

Dependency Pair:

F(s(a), s(b), x) -> F(x, x, x)

Rules:

f(s(a), s(b), x) -> f(x, x, x)
g(f(s(x), s(y), z)) -> g(f(x, y, z))
cons(x, y) -> x
cons(x, y) -> y

Found an infinite P-chain over R:
P =

F(s(a), s(b), x) -> F(x, x, x)

R =

f(s(a), s(b), x) -> f(x, x, x)
g(f(s(x), s(y), z)) -> g(f(x, y, z))
cons(x, y) -> x
cons(x, y) -> y

s = F(cons(s(b), s(a)), cons(s(b), s(a)), cons(s(b), s(a)))
evaluates to t =F(cons(s(b), s(a)), cons(s(b), s(a)), cons(s(b), s(a)))

Thus, s starts an infinite chain.

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