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
↳Argument Filtering and 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))
The following rules can be oriented:
fib(0) -> 0
fib(s(0)) -> s(0)
fib(s(s(x))) -> +(fib(s(x)), fib(x))
Used ordering: Homeomorphic Embedding Order with EMB
resulting in one new DP problem.
Used Argument Filtering System: FIB(x1) -> FIB(x1)
s(x1) -> s(x1)
fib(x1) -> fib(x1)
+(x1, x2) -> x1
R
↳DPs
→DP Problem 1
↳AFS
→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