Term Rewriting System R:
[x, y, z]
cons(x, cons(y, z)) -> big
inf(x) -> cons(x, inf(s(x)))

Termination of R to be shown.

`   R`
`     ↳Dependency Pair Analysis`

R contains the following Dependency Pairs:

INF(x) -> CONS(x, inf(s(x)))
INF(x) -> INF(s(x))

Furthermore, R contains one SCC.

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

Dependency Pair:

INF(x) -> INF(s(x))

Rules:

cons(x, cons(y, z)) -> big
inf(x) -> cons(x, inf(s(x)))

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

INF(x) -> INF(s(x))
one new Dependency Pair is created:

INF(s(x'')) -> INF(s(s(x'')))

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:

INF(s(x'')) -> INF(s(s(x'')))

Rules:

cons(x, cons(y, z)) -> big
inf(x) -> cons(x, inf(s(x)))

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