Term Rewriting System R:
[l, x, k, a, b, c]
f(empty, l) -> l
f(cons(x, k), l) -> g(k, l, cons(x, k))
g(a, b, c) -> f(a, cons(b, c))

Termination of R to be shown.

`   R`
`     ↳Dependency Pair Analysis`

R contains the following Dependency Pairs:

F(cons(x, k), l) -> G(k, l, cons(x, k))
G(a, b, c) -> F(a, cons(b, c))

Furthermore, R contains one SCC.

`   R`
`     ↳DPs`
`       →DP Problem 1`
`         ↳Polynomial Ordering`

Dependency Pairs:

G(a, b, c) -> F(a, cons(b, c))
F(cons(x, k), l) -> G(k, l, cons(x, k))

Rules:

f(empty, l) -> l
f(cons(x, k), l) -> g(k, l, cons(x, k))
g(a, b, c) -> f(a, cons(b, c))

The following dependency pair can be strictly oriented:

G(a, b, c) -> F(a, cons(b, c))

There are no usable rules using the Ce-refinement that need to be oriented.

Used ordering: Polynomial ordering with Polynomial interpretation:
 POL(G(x1, x2, x3)) =  1 + x1 POL(cons(x1, x2)) =  1 + x2 POL(F(x1, x2)) =  x1

resulting in one new DP problem.

`   R`
`     ↳DPs`
`       →DP Problem 1`
`         ↳Polo`
`           →DP Problem 2`
`             ↳Dependency Graph`

Dependency Pair:

F(cons(x, k), l) -> G(k, l, cons(x, k))

Rules:

f(empty, l) -> l
f(cons(x, k), l) -> g(k, l, cons(x, k))
g(a, b, c) -> f(a, cons(b, c))

Using the Dependency Graph resulted in no new DP problems.

Termination of R successfully shown.
Duration:
0:00 minutes