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