Termination Proof Script
Consider the TRS R consisting of the rewrite rules
|
| 1: |
|
f(f(x)) |
→ f(c(f(x))) |
| 2: |
|
f(f(x)) |
→ f(d(f(x))) |
| 3: |
|
g(c(x)) |
→ x |
| 4: |
|
g(d(x)) |
→ x |
| 5: |
|
g(c(0)) |
→ g(d(1)) |
| 6: |
|
g(c(1)) |
→ g(d(0)) |
|
There are 4 dependency pairs:
|
| 7: |
|
F(f(x)) |
→ F(c(f(x))) |
| 8: |
|
F(f(x)) |
→ F(d(f(x))) |
| 9: |
|
G(c(0)) |
→ G(d(1)) |
| 10: |
|
G(c(1)) |
→ G(d(0)) |
|
The approximated dependency graph contains no SCCs
and hence the TRS is trivially terminating.
Tyrolean Termination Tool (0.01 seconds)
--- May 3, 2006