Termination Proof Script
Consider the TRS R consisting of the rewrite rules
|
| 1: |
|
a(b(x)) |
→ b(a(a(x))) |
| 2: |
|
b(c(x)) |
→ c(b(b(x))) |
| 3: |
|
c(a(x)) |
→ a(c(c(x))) |
| 4: |
|
u(a(x)) |
→ x |
| 5: |
|
v(b(x)) |
→ x |
| 6: |
|
w(c(x)) |
→ x |
| 7: |
|
a(u(x)) |
→ x |
| 8: |
|
b(v(x)) |
→ x |
| 9: |
|
c(w(x)) |
→ x |
|
There are 9 dependency pairs:
|
| 10: |
|
A(b(x)) |
→ B(a(a(x))) |
| 11: |
|
A(b(x)) |
→ A(a(x)) |
| 12: |
|
A(b(x)) |
→ A(x) |
| 13: |
|
B(c(x)) |
→ C(b(b(x))) |
| 14: |
|
B(c(x)) |
→ B(b(x)) |
| 15: |
|
B(c(x)) |
→ B(x) |
| 16: |
|
C(a(x)) |
→ A(c(c(x))) |
| 17: |
|
C(a(x)) |
→ C(c(x)) |
| 18: |
|
C(a(x)) |
→ C(x) |
|
The approximated dependency graph contains one SCC:
{10-18}.
-
Consider the SCC {10-18}.
The usable rules are {1-3,7-9}.
The constraints could not be solved.
Tyrolean Termination Tool (0.04 seconds)
--- May 4, 2006