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: Homeomorphic Embedding Order with EMB
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