Term Rewriting System R:
[x, y]
f(x, a) -> x
f(x, g(y)) -> f(g(x), y)
Termination of R to be shown.
R
↳Dependency Pair Analysis
R contains the following Dependency Pairs:
F(x, g(y)) -> F(g(x), y)
Furthermore, R contains one SCC.
R
↳DPs
→DP Problem 1
↳Argument Filtering and Ordering
Dependency Pair:
F(x, g(y)) -> F(g(x), y)
Rules:
f(x, a) -> x
f(x, g(y)) -> f(g(x), y)
The following dependency pair can be strictly oriented:
F(x, g(y)) -> F(g(x), y)
There are no usable rules using the Ce-refinement that need to be oriented.
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, x2) -> x2
g(x1) -> g(x1)
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳Dependency Graph
Dependency Pair:
Rules:
f(x, a) -> x
f(x, g(y)) -> f(g(x), y)
Using the Dependency Graph resulted in no new DP problems.
Termination of R successfully shown.
Duration:
0:00 minutes