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