Term Rewriting System R:
[X]
f(X, g(X)) -> f(1, g(X))
g(1) -> g(0)

Termination of R to be shown.

`   R`
`     ↳Dependency Pair Analysis`

R contains the following Dependency Pairs:

F(X, g(X)) -> F(1, g(X))
G(1) -> G(0)

Furthermore, R contains one SCC.

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

Dependency Pair:

F(X, g(X)) -> F(1, g(X))

Rules:

f(X, g(X)) -> f(1, g(X))
g(1) -> g(0)

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

F(X, g(X)) -> F(1, g(X))
one new Dependency Pair is created:

F(1, g(1)) -> F(1, g(1))

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(1, g(1)) -> F(1, g(1))

Rules:

f(X, g(X)) -> f(1, g(X))
g(1) -> g(0)

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