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

Innermost Termination of R to be shown.

`   R`
`     ↳Dependency Pair Analysis`

R contains the following Dependency Pairs:

F(x) -> F(f(x))
F(x) -> F(x)

Furthermore, R contains one SCC.

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

Dependency Pairs:

F(x) -> F(x)
F(x) -> F(f(x))

Rule:

f(x) -> f(f(x))

Strategy:

innermost

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

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

F(x) -> F(f(f(x)))

The transformation is resulting in one new DP problem:

`   R`
`     ↳DPs`
`       →DP Problem 1`
`         ↳Rw`
`           →DP Problem 2`
`             ↳Narrowing Transformation`

Dependency Pairs:

F(x) -> F(f(f(x)))
F(x) -> F(x)

Rule:

f(x) -> f(f(x))

Strategy:

innermost

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

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

F(x'') -> F(f(f(f(x''))))

The transformation is resulting in one new DP problem:

`   R`
`     ↳DPs`
`       →DP Problem 1`
`         ↳Rw`
`           →DP Problem 2`
`             ↳Nar`
`             ...`
`               →DP Problem 3`
`                 ↳Remaining Obligation(s)`

The following remains to be proven:
Dependency Pairs:

F(x'') -> F(f(f(f(x''))))
F(x) -> F(x)

Rule:

f(x) -> f(f(x))

Strategy:

innermost

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