Term Rewriting System R:
[X]
f(f(X)) -> f(g(f(g(f(X)))))
f(g(f(X))) -> f(g(X))
Termination of R to be shown.
R
↳Dependency Pair Analysis
R contains the following Dependency Pairs:
F(f(X)) -> F(g(f(g(f(X)))))
F(f(X)) -> F(g(f(X)))
F(g(f(X))) -> F(g(X))
Furthermore, R contains one SCC.
R
↳DPs
→DP Problem 1
↳Polynomial Ordering
Dependency Pair:
F(g(f(X))) -> F(g(X))
Rules:
f(f(X)) -> f(g(f(g(f(X)))))
f(g(f(X))) -> f(g(X))
The following dependency pair can be strictly oriented:
F(g(f(X))) -> F(g(X))
There are no usable rules w.r.t. to the implicit AFS that need to be oriented.
Used ordering: Polynomial ordering with Polynomial interpretation:
| POL(g(x1)) | = x1 |
| POL(F(x1)) | = 1 + x1 |
| POL(f(x1)) | = 1 + x1 |
resulting in one new DP problem.
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Dependency Graph
Dependency Pair:
Rules:
f(f(X)) -> f(g(f(g(f(X)))))
f(g(f(X))) -> f(g(X))
Using the Dependency Graph resulted in no new DP problems.
Termination of R successfully shown.
Duration:
0:00 minutes