Termination Proof Script
Consider the TRS R consisting of the rewrite rules
|
| 1: |
|
fib(0) |
→ 0 |
| 2: |
|
fib(s(0)) |
→ s(0) |
| 3: |
|
fib(s(s(x))) |
→ fib(s(x)) + fib(x) |
|
There are 2 dependency pairs:
|
| 4: |
|
FIB(s(s(x))) |
→ FIB(s(x)) |
| 5: |
|
FIB(s(s(x))) |
→ FIB(x) |
|
The approximated dependency graph contains one SCC:
{4,5}.
-
Consider the SCC {4,5}.
There are no usable rules.
By taking the AF π with
π(FIB) = 1 together with
the lexicographic path order with
empty precedence,
the rules in {4,5}
are strictly decreasing.
Hence the TRS is terminating.
Tyrolean Termination Tool (0.00 seconds)
--- May 3, 2006