Term Rewriting System R:
[X, Y]
f(g(X), Y) -> f(X, f(g(X), Y))
Termination of R to be shown.
R
↳Dependency Pair Analysis
R contains the following Dependency Pairs:
F(g(X), Y) -> F(X, f(g(X), Y))
F(g(X), Y) -> F(g(X), Y)
Furthermore, R contains one SCC.
R
↳DPs
→DP Problem 1
↳Polynomial Ordering
Dependency Pairs:
F(g(X), Y) -> F(g(X), Y)
F(g(X), Y) -> F(X, f(g(X), Y))
Rule:
f(g(X), Y) -> f(X, f(g(X), Y))
The following dependency pair can be strictly oriented:
F(g(X), Y) -> F(X, f(g(X), Y))
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)) | = 1 + x1 |
| POL(f(x1, x2)) | = 0 |
| POL(F(x1, x2)) | = x1 |
resulting in one new DP problem.
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Remaining Obligation(s)
The following remains to be proven:
Dependency Pair:
F(g(X), Y) -> F(g(X), Y)
Rule:
f(g(X), Y) -> f(X, f(g(X), Y))
Termination of R could not be shown.
Duration:
0:00 minutes