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

Innermost Termination of R to be shown. 



   R
     ↳Dependency Pair Analysis



R contains the following Dependency Pairs:

A -> G(c)
F(g(X), b) -> F(a, X)
F(g(X), b) -> A

Furthermore, R contains one SCC. 


   R
     ↳DPs
       →DP Problem 1
         ↳Narrowing Transformation


Dependency Pair:

F(g(X), b) -> F(a, X)


Rules:


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


Strategy:

innermost




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

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

F(g(X), b) -> F(g(c), X)

The transformation is resulting in one new DP problem: 



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




The following remains to be proven:
Dependency Pair:

F(g(X), b) -> F(g(c), X)


Rules:


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


Strategy:

innermost



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