Termination Proof Script
Consider the TRS R consisting of the rewrite rules
|
| 1: |
|
x + 0 |
→ x |
| 2: |
|
x + s(y) |
→ s(x + y) |
| 3: |
|
0 + y |
→ y |
| 4: |
|
s(x) + y |
→ s(x + y) |
| 5: |
|
x + (y + z) |
→ (x + y) + z |
| 6: |
|
f(g(f(x))) |
→ f(h(s(0),x)) |
| 7: |
|
f(g(h(x,y))) |
→ f(h(s(x),y)) |
| 8: |
|
f(h(x,h(y,z))) |
→ f(h(x + y,z)) |
|
There are 8 dependency pairs:
|
| 9: |
|
x +# s(y) |
→ x +# y |
| 10: |
|
s(x) +# y |
→ x +# y |
| 11: |
|
x +# (y + z) |
→ (x + y) +# z |
| 12: |
|
x +# (y + z) |
→ x +# y |
| 13: |
|
F(g(f(x))) |
→ F(h(s(0),x)) |
| 14: |
|
F(g(h(x,y))) |
→ F(h(s(x),y)) |
| 15: |
|
F(h(x,h(y,z))) |
→ F(h(x + y,z)) |
| 16: |
|
F(h(x,h(y,z))) |
→ x +# y |
|
The approximated dependency graph contains 2 SCCs:
{9-12}
and {15}.
-
Consider the SCC {9-12}.
The usable rules are {1-5}.
The constraints could not be solved.
-
Consider the SCC {15}.
The usable rules are {1-5}.
The constraints could not be solved.
Tyrolean Termination Tool (0.02 seconds)
--- May 4, 2006