Term Rewriting System R:
[x, y, z]
f(x, y, z) -> g(x, y, z)
g(0, 1, x) -> f(x, x, x)
a -> b
a -> c

Termination of R to be shown.

`   R`
`     ↳Dependency Pair Analysis`

R contains the following Dependency Pairs:

F(x, y, z) -> G(x, y, z)
G(0, 1, x) -> F(x, x, x)

Furthermore, R contains one SCC.

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

Dependency Pairs:

G(0, 1, x) -> F(x, x, x)
F(x, y, z) -> G(x, y, z)

Rules:

f(x, y, z) -> g(x, y, z)
g(0, 1, x) -> f(x, x, x)
a -> b
a -> c

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

F(x, y, z) -> G(x, y, z)
one new Dependency Pair is created:

F(0, 1, z') -> G(0, 1, z')

The transformation is resulting in one new DP problem:

`   R`
`     ↳DPs`
`       →DP Problem 1`
`         ↳FwdInst`
`           →DP Problem 2`
`             ↳Forward Instantiation Transformation`

Dependency Pairs:

F(0, 1, z') -> G(0, 1, z')
G(0, 1, x) -> F(x, x, x)

Rules:

f(x, y, z) -> g(x, y, z)
g(0, 1, x) -> f(x, x, x)
a -> b
a -> c

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

G(0, 1, x) -> F(x, x, x)
no new Dependency Pairs are created.
The transformation is resulting in no new DP problems.

Termination of R successfully shown.
Duration:
0:00 minutes