Term Rewriting System R:
[x]
f(h(x)) -> f(i(x))
f(i(x)) -> a
i(x) -> h(x)

Innermost Termination of R to be shown.

`   R`
`     ↳Dependency Pair Analysis`

R contains the following Dependency Pairs:

F(h(x)) -> F(i(x))
F(h(x)) -> I(x)

Furthermore, R contains one SCC.

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

Dependency Pair:

F(h(x)) -> F(i(x))

Rules:

f(h(x)) -> f(i(x))
f(i(x)) -> a
i(x) -> h(x)

Strategy:

innermost

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

F(h(x)) -> F(i(x))
one new Dependency Pair is created:

F(h(x)) -> F(h(x))

The transformation is resulting in one new DP problem:

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

The following remains to be proven:
Dependency Pair:

F(h(x)) -> F(h(x))

Rules:

f(h(x)) -> f(i(x))
f(i(x)) -> a
i(x) -> h(x)

Strategy:

innermost

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