Term Rewriting System R:
[X, Y]
f(X, g(X), Y) -> f(Y, Y, Y)
g(b) -> c
b -> c

Termination of R to be shown.

`   R`
`     ↳Dependency Pair Analysis`

R contains the following Dependency Pairs:

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

Furthermore, R contains one SCC.

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

Dependency Pair:

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

Rules:

f(X, g(X), Y) -> f(Y, Y, Y)
g(b) -> c
b -> c

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

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

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

The transformation is resulting in one new DP problem:

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

The following remains to be proven:
Dependency Pair:

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

Rules:

f(X, g(X), Y) -> f(Y, Y, Y)
g(b) -> c
b -> c

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