Term Rewriting System R:
[X, Y]
f(X) -> if(X, c, f(true))
if(true, X, Y) -> X
if(false, X, Y) -> Y

Termination of R to be shown.

`   R`
`     ↳Dependency Pair Analysis`

R contains the following Dependency Pairs:

F(X) -> IF(X, c, f(true))
F(X) -> F(true)

Furthermore, R contains one SCC.

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

Dependency Pair:

F(X) -> F(true)

Rules:

f(X) -> if(X, c, f(true))
if(true, X, Y) -> X
if(false, X, Y) -> Y

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

F(X) -> F(true)
one new Dependency Pair is created:

F(true) -> F(true)

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(true) -> F(true)

Rules:

f(X) -> if(X, c, f(true))
if(true, X, Y) -> X
if(false, X, Y) -> Y

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