Term Rewriting System R:
[X]
g(X) -> h(X)
c -> d
h(d) -> g(c)

Innermost Termination of R to be shown.

`   R`
`     ↳Dependency Pair Analysis`

R contains the following Dependency Pairs:

G(X) -> H(X)
H(d) -> G(c)
H(d) -> C

Furthermore, R contains one SCC.

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

Dependency Pairs:

H(d) -> G(c)
G(X) -> H(X)

Rules:

g(X) -> h(X)
c -> d
h(d) -> g(c)

Strategy:

innermost

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

H(d) -> G(c)
one new Dependency Pair is created:

H(d) -> G(d)

The transformation is resulting in one new DP problem:

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

Dependency Pairs:

H(d) -> G(d)
G(X) -> H(X)

Rules:

g(X) -> h(X)
c -> d
h(d) -> g(c)

Strategy:

innermost

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

G(X) -> H(X)
one new Dependency Pair is created:

G(d) -> H(d)

The transformation is resulting in one new DP problem:

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

The following remains to be proven:
Dependency Pairs:

G(d) -> H(d)
H(d) -> G(d)

Rules:

g(X) -> h(X)
c -> d
h(d) -> g(c)

Strategy:

innermost

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