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