Termination Proof Script
Consider the TRS R consisting of the rewrite rules
|
| 1: |
|
and(x,false) |
→ false |
| 2: |
|
and(x,not(false)) |
→ x |
| 3: |
|
not(not(x)) |
→ x |
| 4: |
|
implies(false,y) |
→ not(false) |
| 5: |
|
implies(x,false) |
→ not(x) |
| 6: |
|
implies(not(x),not(y)) |
→ implies(y,and(x,y)) |
|
There are 4 dependency pairs:
|
| 7: |
|
IMPLIES(false,y) |
→ NOT(false) |
| 8: |
|
IMPLIES(x,false) |
→ NOT(x) |
| 9: |
|
IMPLIES(not(x),not(y)) |
→ IMPLIES(y,and(x,y)) |
| 10: |
|
IMPLIES(not(x),not(y)) |
→ AND(x,y) |
|
The approximated dependency graph contains one SCC:
{9}.
-
Consider the SCC {9}.
The usable rules are {1,2}.
The constraints could not be solved.
Tyrolean Termination Tool (0.01 seconds)
--- May 4, 2006