Term Rewriting System R:
[X]
f(g(X)) -> f(X)

Termination of R to be shown. 



   R
     ↳Dependency Pair Analysis



R contains the following Dependency Pairs:

F(g(X)) -> F(X)

Furthermore, R contains one SCC. 


   R
     ↳DPs
       →DP Problem 1
         ↳Argument Filtering and Ordering


Dependency Pair:

F(g(X)) -> F(X)


Rule:


f(g(X)) -> f(X)





The following dependency pair can be strictly oriented:

F(g(X)) -> F(X)


The following rule can be oriented:

f(g(X)) -> f(X)


Used ordering: Lexicographic Path Order with Non-Strict Precedence with Quasi Precedence:
trivial

resulting in one new DP problem.
Used Argument Filtering System:
F(x1) -> F(x1)
g(x1) -> g(x1)
f(x1) -> f(x1)


   R
     ↳DPs
       →DP Problem 1
         ↳AFS
           →DP Problem 2
             ↳Dependency Graph


Dependency Pair:


Rule:


f(g(X)) -> f(X)





Using the Dependency Graph resulted in no new DP problems.

Termination of R successfully shown.
Duration:
0:00 minutes