Termination Proof Script
Consider the TRS R consisting of the rewrite rules
|
| 1: |
|
p(s(x)) |
→ x |
| 2: |
|
fact(0) |
→ s(0) |
| 3: |
|
fact(s(x)) |
→ s(x) * fact(p(s(x))) |
| 4: |
|
0 * y |
→ 0 |
| 5: |
|
s(x) * y |
→ (x * y) + y |
| 6: |
|
x + 0 |
→ x |
| 7: |
|
x + s(y) |
→ s(x + y) |
|
There are 6 dependency pairs:
|
| 8: |
|
FACT(s(x)) |
→ s(x) *# fact(p(s(x))) |
| 9: |
|
FACT(s(x)) |
→ FACT(p(s(x))) |
| 10: |
|
FACT(s(x)) |
→ P(s(x)) |
| 11: |
|
s(x) *# y |
→ (x * y) +# y |
| 12: |
|
s(x) *# y |
→ x *# y |
| 13: |
|
x +# s(y) |
→ x +# y |
|
The approximated dependency graph contains 3 SCCs:
{13},
{12}
and {9}.
-
Consider the SCC {13}.
There are no usable rules.
By taking the AF π with
π(+#) = 2 together with
the lexicographic path order with
empty precedence,
rule 13
is strictly decreasing.
-
Consider the SCC {12}.
There are no usable rules.
By taking the AF π with
π(*#) = 1 together with
the lexicographic path order with
empty precedence,
rule 12
is strictly decreasing.
-
Consider the SCC {9}.
The usable rules are {1}.
The constraints could not be solved.
Tyrolean Termination Tool (0.02 seconds)
--- May 3, 2006