Term Rewriting System R:
[x, y]
f(g(x), y, y) -> g(f(x, x, y))
Termination of R to be shown.
R
↳Dependency Pair Analysis
R contains the following Dependency Pairs:
F(g(x), y, y) -> F(x, x, y)
Furthermore, R contains one SCC.
R
↳DPs
→DP Problem 1
↳Argument Filtering and Ordering
Dependency Pair:
F(g(x), y, y) -> F(x, x, y)
Rule:
f(g(x), y, y) -> g(f(x, x, y))
The following dependency pair can be strictly oriented:
F(g(x), y, y) -> F(x, x, y)
The following rule can be oriented:
f(g(x), y, y) -> g(f(x, x, y))
Used ordering: Homeomorphic Embedding Order with EMB
resulting in one new DP problem.
Used Argument Filtering System: F(x1, x2, x3) -> x1
g(x1) -> g(x1)
f(x1, x2, x3) -> x1
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳Dependency Graph
Dependency Pair:
Rule:
f(g(x), y, y) -> g(f(x, x, y))
Using the Dependency Graph resulted in no new DP problems.
Termination of R successfully shown.
Duration:
0:00 minutes