Termination Proof Script
Consider the TRS R consisting of the rewrite rules
|
| 1: |
|
fac(s(x)) |
→ fac(p(s(x))) * s(x) |
| 2: |
|
p(s(0)) |
→ 0 |
| 3: |
|
p(s(s(x))) |
→ s(p(s(x))) |
|
There are 3 dependency pairs:
|
| 4: |
|
FAC(s(x)) |
→ FAC(p(s(x))) |
| 5: |
|
FAC(s(x)) |
→ P(s(x)) |
| 6: |
|
P(s(s(x))) |
→ P(s(x)) |
|
The approximated dependency graph contains 2 SCCs:
{6}
and {4}.
-
Consider the SCC {6}.
There are no usable rules.
By taking the AF π with
π(P) = 1 together with
the lexicographic path order with
empty precedence,
rule 6
is strictly decreasing.
-
Consider the SCC {4}.
The usable rules are {2,3}.
The constraints could not be solved.
Tyrolean Termination Tool (0.01 seconds)
--- May 4, 2006