Termination Proof Script
Consider the TRS R consisting of the rewrite rules
|
| 1: |
|
implies(not(x),y) |
→ or(x,y) |
| 2: |
|
implies(not(x),or(y,z)) |
→ implies(y,or(x,z)) |
| 3: |
|
implies(x,or(y,z)) |
→ or(y,implies(x,z)) |
|
There are 2 dependency pairs:
|
| 4: |
|
IMPLIES(not(x),or(y,z)) |
→ IMPLIES(y,or(x,z)) |
| 5: |
|
IMPLIES(x,or(y,z)) |
→ IMPLIES(x,z) |
|
The approximated dependency graph contains one SCC:
{4,5}.
-
Consider the SCC {4,5}.
There are no usable rules.
By taking the AF π with
π(IMPLIES) = 2
and π(or) = [2] together with
the lexicographic path order with
empty precedence,
rule 4
is weakly decreasing and
rule 5
is strictly decreasing.
There is one new SCC.
-
Consider the SCC {4}.
The constraints could not be solved.
Tyrolean Termination Tool (0.01 seconds)
--- May 4, 2006