Term Rewriting System R:
[x, y]
g(x, y) -> x
g(x, y) -> y
f(s(x), y, y) -> f(y, x, s(x))
Termination of R to be shown.
R
↳Dependency Pair Analysis
R contains the following Dependency Pairs:
F(s(x), y, y) -> F(y, x, s(x))
Furthermore, R contains one SCC.
R
↳DPs
→DP Problem 1
↳Polynomial Ordering
Dependency Pair:
F(s(x), y, y) -> F(y, x, s(x))
Rules:
g(x, y) -> x
g(x, y) -> y
f(s(x), y, y) -> f(y, x, s(x))
The following dependency pair can be strictly oriented:
F(s(x), y, y) -> F(y, x, s(x))
Additionally, the following rules can be oriented:
g(x, y) -> x
g(x, y) -> y
f(s(x), y, y) -> f(y, x, s(x))
Used ordering: Polynomial ordering with Polynomial interpretation:
| POL(g(x1, x2)) | = x1 + x2 |
| POL(s(x1)) | = 1 + x1 |
| POL(f(x1, x2, x3)) | = 0 |
| POL(F(x1, x2, x3)) | = x1 + x2 |
resulting in one new DP problem.
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Dependency Graph
Dependency Pair:
Rules:
g(x, y) -> x
g(x, y) -> y
f(s(x), y, y) -> f(y, x, s(x))
Using the Dependency Graph resulted in no new DP problems.
Termination of R successfully shown.
Duration:
0:00 minutes