Termination Proof Script
Consider the TRS R consisting of the rewrite rules
|
| 1: |
|
X + 0 |
→ X |
| 2: |
|
X + s(Y) |
→ s(X + Y) |
| 3: |
|
double(X) |
→ X + X |
| 4: |
|
f(0,s(0),X) |
→ f(X,double(X),X) |
| 5: |
|
g(X,Y) |
→ X |
| 6: |
|
g(X,Y) |
→ Y |
|
There are 4 dependency pairs:
|
| 7: |
|
X +# s(Y) |
→ X +# Y |
| 8: |
|
DOUBLE(X) |
→ X +# X |
| 9: |
|
F(0,s(0),X) |
→ F(X,double(X),X) |
| 10: |
|
F(0,s(0),X) |
→ DOUBLE(X) |
|
The approximated dependency graph contains 2 SCCs:
{7}
and {9}.
-
Consider the SCC {7}.
There are no usable rules.
By taking the AF π with
π(+#) = 2 together with
the lexicographic path order with
empty precedence,
rule 7
is strictly decreasing.
-
Consider the SCC {9}.
The usable rules are {1-3}.
The constraints could not be solved.
Tyrolean Termination Tool (0.01 seconds)
--- May 4, 2006