Term Rewriting System R:
[x, y]
f(s(x), y, y) -> f(y, x, s(x))

Termination of R to be shown.

`   R`
`     ↳Dependency Pair Analysis`

R contains the following Dependency Pairs:

F(s(x), y, y) -> F(y, x, s(x))

Furthermore, R contains one SCC.

`   R`
`     ↳DPs`
`       →DP Problem 1`
`         ↳Instantiation Transformation`

Dependency Pair:

F(s(x), y, y) -> F(y, x, s(x))

Rule:

f(s(x), y, y) -> f(y, x, s(x))

On this DP problem, an Instantiation SCC transformation can be performed.
As a result of transforming the rule

F(s(x), y, y) -> F(y, x, s(x))
one new Dependency Pair is created:

F(s(x0), s(x'''), s(x''')) -> F(s(x'''), x0, s(x0))

The transformation is resulting in one new DP problem:

`   R`
`     ↳DPs`
`       →DP Problem 1`
`         ↳Inst`
`           →DP Problem 2`
`             ↳Remaining Obligation(s)`

The following remains to be proven:
Dependency Pair:

F(s(x0), s(x'''), s(x''')) -> F(s(x'''), x0, s(x0))

Rule:

f(s(x), y, y) -> f(y, x, s(x))

Termination of R could not be shown.
Duration:
0:00 minutes