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

Innermost 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


Strategy:

innermost




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


Strategy:

innermost



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