Termination Proof Script
Consider the TRS R consisting of the rewrite rules
|
| 1: |
|
not(true) |
→ false |
| 2: |
|
not(false) |
→ true |
| 3: |
|
evenodd(x,0) |
→ not(evenodd(x,s(0))) |
| 4: |
|
evenodd(0,s(0)) |
→ false |
| 5: |
|
evenodd(s(x),s(0)) |
→ evenodd(x,0) |
|
There are 3 dependency pairs:
|
| 6: |
|
EVENODD(x,0) |
→ NOT(evenodd(x,s(0))) |
| 7: |
|
EVENODD(x,0) |
→ EVENODD(x,s(0)) |
| 8: |
|
EVENODD(s(x),s(0)) |
→ EVENODD(x,0) |
|
The approximated dependency graph contains one SCC:
{7,8}.
-
Consider the SCC {7,8}.
There are no usable rules.
By taking the AF π with
π(EVENODD) = 1 together with
the lexicographic path order with
empty precedence,
rule 7
is weakly decreasing and
rule 8
is strictly decreasing.
Hence the TRS is terminating.
Tyrolean Termination Tool (0.01 seconds)
--- May 3, 2006