Term Rewriting System R:
[x]
f(f(x)) -> f(x)
g(0) -> g(f(0))
Termination of R to be shown.
R
↳Dependency Pair Analysis
R contains the following Dependency Pairs:
G(0) -> G(f(0))
G(0) -> F(0)
Furthermore, R contains one SCC.
R
↳DPs
→DP Problem 1
↳Argument Filtering and Ordering
Dependency Pair:
G(0) -> G(f(0))
Rules:
f(f(x)) -> f(x)
g(0) -> g(f(0))
The following dependency pair can be strictly oriented:
G(0) -> G(f(0))
The following usable rule w.r.t. to the AFS can be oriented:
f(f(x)) -> f(x)
Used ordering: Lexicographic Path Order with Non-Strict Precedence with Quasi Precedence:
0 > f
resulting in one new DP problem.
Used Argument Filtering System: G(x1) -> G(x1)
f(x1) -> f
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳Dependency Graph
Dependency Pair:
Rules:
f(f(x)) -> f(x)
g(0) -> g(f(0))
Using the Dependency Graph resulted in no new DP problems.
Termination of R successfully shown.
Duration:
0:00 minutes